title: Endemol Shine Group

text: In November 2021, it was announced that Endemol Shine will be moving into podcasting for the first time with a partnership with KT Studios with the aim of developing and co-producing original podcasts.


title: Documenta

text: documenta is an exhibition of contemporary art which takes place every five years in Kassel, Germany.


title: Documenta

text: The "documenta" was founded by artist, teacher and curator Arnold Bode in 1955 as part of the Bundesgartenschau (Federal Horticultural Show) which took place in Kassel at that time. It was an attempt to bring Germany up to speed with modern art, both banishing and repressing the cultural darkness of Nazism. This first "documenta" featured many artists who are generally considered to have had a significant influence on modern art (such as Picasso and Kandinsky). The more recent editions of the event feature artists based across the world, but much of the art is site-specific.


title: Documenta

text: Every "documenta" is limited to 100 days of exhibition, which is why it is often referred to as the "museum of 100 days". "Documenta" is not a selling exhibition.


title: Documenta

text: The name of the exhibition is an invented word. The term is supposed to demonstrate the intention of every exhibition (in particular of the first "documenta" in 1955) to be a documentation of modern art which was not available for the German public during the Nazi era. Rumour spread from those close to Arnold Bode that it was relevant for the coinage of the term that the Latin word "" could be separated into "" (Latin for 'teach') and "" (Latin for 'intellect') and therefore thought it to be a good word to describe the intention and the demand of the "documenta".


title: Documenta

text: Each edition of "documenta" has commissioned its own visual identity, most of which have conformed to the typographic style of solely using lowercase letters, which originated at the Bauhaus.


title: Documenta

text: Art professor and designer Arnold Bode from Kassel was the initiator of the first "documenta". Originally planned as a secondary event to accompany the Bundesgartenschau, this attracted more than 130,000 visitors in 1955. The exhibition centred less on "contemporary art“, that is art made after 1945: instead, Bode wanted to show the public works which had been known as "Entartete Kunst" in Germany during the Nazi era: Fauvism, Expressionism, Cubism, Blauer Reiter, Futurism and Pittura Metafisica. Therefore, abstract art, in particular the abstract paintings of the 1920s and 1930s, was the focus of interest in this exhibition.


title: Documenta

text: Over time, the focus shifted to contemporary art. At first, the show was limited to works from Europe, but soon covered works by artists from the Americas, Africa and Asia. "4. documenta", the first ever to turn a profit, featured a selection of Pop Art, Minimal Art, and Kinetic Art. Adopting the theme of "Questioning Reality – Pictorial Worlds Today," the 1972 "documenta" radically redefined what could be considered art by featuring minimal and conceptual art, marking a turning point in the public acceptance of those styles. Also, it devoted a large section to the work of Adolf Wolfli, the great Swiss outsider, then unknown. Joseph Beuys performed repeatedly under the auspices of his utopian Organization for Direct Democracy. Additionally, the 1987 "documenta" show signaled another important shift with the elevation of design to the realm of art – showing an openness to postmodern design. Certain key political dates for wide-reaching social and cultural upheavals, such as 1945, 1968 or 1976/1977, became chronological markers of "documenta X" (1997), along which art's political, social, cultural and aesthetic exploratory functions were traced. "Documenta11" was organized around themes like migration, urbanization and the post-colonial experience, with documentary photography, film and video as well as works from far-flung locales holding the spotlight. In 2012, "documenta (13)" was described as "[a]rdently feminist, global and multimedia in approach and including works by dead artists and selected bits of ancient art".


title: Documenta

text: "documenta" typically gives its artists at least two years to conceive and produce their projects, so the works are often elaborate and intellectually complex. However, the participants are often not publicised before the very opening of the exhibition. At "documenta (13)", the official list of artists was not released until the day the show opened. Even though curators have often claimed to have gone outside the art market in their selection, participants have always included established artists. In the "documenta (13)", for example, art critic Jerry Saltz identified more than a third of the artists represented by Marian Goodman Gallery in the show.


title: Documenta

text: In 2022, "documenta" caused three separate anti-Semitism controversies: one revolving around the banner "Peopleʼs Justice" (2002) by the Indonesian collective Taring Padi that contained anti-Semitic imagery; another on the inclusion of the Palestinian collective Question of Funding in the exhibition; and, lastly, the inclusion of a 1988 Palestinian liberation movement brochure by Burhan Karkoutly titled "Presence des Femmes". Artist Hito Steyerl pulled her work from the exhibition in protest to the first two instances, with managing director Sabine Schormann's departure as a consequence. In response to the controversy spurred by "Presence des Femmes", "documenta" released a statement urging the artistic team to remove the drawings until they can be “appropriately contextualized"; scholars from the Archives of Women’s Struggles in Algeria stated: "["Presence des Femmes"] was in solidarity by the Algerian women with the Palestinian people, in denouncing the crimes committed by the Israeli State. We would like this document, like many other texts or artworks in the world, to be placed in its historical and political context."


title: Documenta

text: The first four "documentas", organized by Arnold Bode, established the exhibition's international credentials. Since the fifth "documenta" (1972), a new artistic director has been named for each "documenta" exhibition by a committee of experts. "Documenta 8" was put together in two years instead of the usual five. The original directors, Edy de Wilde and Harald Szeemann, were unable to get along and stepped down. They were replaced by Manfred Schneckenburger, Edward F. Fry, Wulf Herzogenrath, Armin Zweite, and Vittorio Fagone. Coosje van Bruggen helped select artists for "documenta 7", the 1982 edition. "documenta IX"'s team of curators consisted of Jan Hoet, Piero Luigi Tazzi, Denys Zacharopoulos, and Bart de Baere. For "documenta X" Catherine David was chosen as the first woman and the first non-German speaker to hold the post. It is also the first and unique time that its website Documenta x was conceived by a curator (swiss curator Simon Lamunière) as a part of the exhibition. The first non-European director was Okwui Enwezor for "Documenta11".


title: Documenta

text: 2012's edition was organized around a central node, the trans-Atlantic melding of two distinct individuals who first encountered each other in the "money-soaked deserts of the United Arab Emirates". As an organizing principle it is simultaneously a commentary on the romantic potentials of globalization and also a critique of how digital platforms can complicate or interrogate the nature of such relationships. Curatorial agents refer to the concept as possessing a "fricative potential for productive awkwardness," wherein a twosome is formed for the purposes of future exploration.


title: Documenta

text: "documenta" is held in different venues in Kassel. Since 1955, the fixed venue has been the Fridericianum. The documenta-Halle was built in 1992 for "documenta IX" and now houses some of the exhibitions. Other venues used for "documenta" have included the Karlsaue park, Schloss Wilhelmshöhe, the Neue Galerie, the Ottoneum, and the Kulturzentrum Schlachthof. Though Okwui Enezor notably tried to subvert the euro-centric approach "documenta" had taken, he instigated a series of five platforms before the "Documenta11" in Vienna, Berlin, New Delhi, St Lucia, and Lagos, in an attempt to take "documenta" into a new post-colonial, borderless space, from which experimental cultures could emerge. "documenta 12" occupied five locations, including the Fridericianum, the Wilhelmshöhe castle park and the specially constructed "Aue-Pavillon", or meadow pavilion, designed by French firm Lacaton et Vassal. At "documenta (13)" (2012), about a fifth of the works were unveiled in places like Kabul, Afghanistan, and Banff, Canada.


title: Documenta

text: There are also a number of works that are usually presented outside, most notably in Friedrichsplatz, in front of the Fridericianum, and the Karlsaue park. To handle the number of artworks at "documenta IX", five connected temporary "trailers" in glass and corrugated metal were built in the Karlsaue. For "documenta (13)", French architects Anne Lacaton and Jean-Philippe Vassal constructed the temporary "Aue-Pavillon" in the park.


title: Documenta

text: A few of the works exhibited at various "documentas" remained as purchases in Kassel museums. They include "7000 Eichen" by Joseph Beuys; "Rahmenbau" (1977) by Haus-Rucker-Co; "Laserscape Kassel" (1977) by Horst H. Baumann; "Traumschiff Tante Olga" (1977) by Anatol Herzfeld; "Vertikaler Erdkilometer" by Walter De Maria; "Spitzhacke" (1982) by Claes Oldenburg; "Man walking to the sky" (1992) by Jonathan Borofsky; and "Fremde" (1992) by Thomas Schütte (one part of the sculptures are installed on Rotes Palais at Friedrichsplatz, the other on the roof of the Concert Hall in Lübeck).


title: Documenta

text: The extensive volume of material that is regularly generated on the occasion of this exhibition prompted Arnold Bode to create an archive in 1961. The heart of the archive’s collection comes from the files and materials of the documenta organization. A continually expanding video and image archive is also part of the collection as are the independently organized bequests of Arnold Bode and artist Harry Kramer.


title: Documenta

text: In 1992, on the occasion of "documenta IX", for the first time in the history of the "documenta", more than half a million people traveled to Kassel. The 2002 edition of "documenta" attracted 650,000 visitors, more than triple Kassel's population. In 2007, "documenta 12" drew 754,000 paying visitors, with more than one-third of the visitors coming from abroad and guests from neighboring Netherlands, France, Belgium and Austria among the most numerous. In 2012, "documenta (13)" had 904,992 visitors.


title: Documenta

text: In 2007, half of "documenta"'s budget of 19 million euros ($25.7 million) came from the city of Kassel, the state of Hessen and Germany's Kulturstiftung des Bundes. The rest came from sponsors, donors, and ticket sales.


title: Documenta

text: Documenta 14’s budget was at 37 million euros ($40 million), spread between 2013 and 2018; by the end of 2017, its deficit was expected to reach 5.4 million euros. Overspending in Athens led to a liquidity shortfall of 7 million euros, forcing the shareholders of Documenta — the city of Kassel and the German state of Hesse — to step in with emergency loan guarantees worth 8 million euros.


title: Carlos Salcedo

text: Carlos Joel Salcedo Hernández (born 29 September 1993), also known as El Titán, is a Mexican professional footballer who plays as a centre-back for Liga MX club Juárez.


title: Carlos Salcedo

text: Salcedo began his youth career at Guadalajara in 2006 and moved to Tigres UANL and then Real Salt Lake, where he started his professional career in 2013. He would return to Guadalajara in 2015, and the following year made his move abroad with loan spells at Fiorentina and Eintracht Frankfurt, making a permanent move with the latter in 2018.


title: Carlos Salcedo

text: A Mexican international since 2015, Salcedo has represented Mexico at the 2015 Copa América and Copa América Centenario, the 2019 CONCACAF Gold Cup, the 2016 Summer Olympics, the 2017 FIFA Confederations Cup, and the 2018 FIFA World Cup.


title: Carlos Salcedo

text: Having previously played at C.D. Guadalajara's and Tigres UANL's youth academy teams, Salcedo joined Major League Soccer (MLS) club Real Salt Lake's academy in January 2012. In August of the same year he began training with the first-team squad. Salcedo signed a home grown player contract with Salt Lake in January 2013, having met the minimum requirement to be defined as "home grown" of one year academy training.


title: Carlos Salcedo

text: On 4 May 2013, Salcedo made his professional MLS debut for Real Salt Lake as a substitute against Vancouver Whitecaps, ending in a 2–0 win entering as a substitute in the 89th minute. In the second half of the 2013 season he was a regular starter for Salt Lake starting 12 games by season's end.


title: Carlos Salcedo

text: Following a lack of playing time in the 2014 season with Real Salt Lake, in November 2014, Salcedo took to Twitter asking the team not to bring him into future team plans, citing issues with former general manager Garth Lagerwey.


title: Carlos Salcedo

text: On 6 January 2015, Salcedo returned to Mexican side C.D. Guadalajara, for the price of $450,000. Salcedo made his debut for the club in a 2–1 win at home against Pumas UNAM in which he played the first 60 minutes.


title: Carlos Salcedo

text: On 1 March, Salcedo scored his first goal in a 3–0 win at home against Monterrey in which he played the full 90 minutes. At the end of his first tournament with "Chivas", he was listed in the Best XI.


title: Carlos Salcedo

text: The following season, he would win the Apertura 2015 Copa MX with Guadalajara, defeating Club León 1–0, qualifying them to the 2016 Supercopa MX, where they would also go on to win, defeating Veracruz 2–0.


title: Carlos Salcedo

text: On 21 August 2016, Italian club ACF Fiorentina announced they had acquired Salcedo on loan, with the option to purchase the player at the end of the deal. Salcedo made his debut with Fiorentina on 15 September against PAOK in their 0–0 draw in the Europa League. He made his Serie A debut ten days later against Milan in a 0–0 draw.


title: Carlos Salcedo

text: On 13 June 2017, Salcedo joined German side Eintracht Frankfurt on an initial loan from Guadalajara with an option to buy. Following a shoulder injury sustained at the 2017 FIFA Confederations Cup, Salcedo's Bundesliga debut came on 9 September against Borussia Mönchengladbach which ended in a 1–0 win for Eintracht Frankfurt, playing the entirety of the match.


title: Carlos Salcedo

text: In April 2018, Salcedo was listed as one of three center-backs nominated for the Bundesliga "Team of the Season", alongside Mats Hummels and Jerome Boateng. On 14 May, Eintracht Frankfurt announced they had signed Salcedo to a four-year contract, tying him to the club until 2022. On 19 May, Salcedo won the DFB-Pokal with Eintracht Frankfurt after they defeated Bayern Munich 3–1 in the final.


title: Carlos Salcedo

text: On 12 August 2018, Salcedo played in his first competitive game of the season in Frankfurt's 5–0 loss to Bayern Munich for the DFL-Supercup. On 1 September, during a league match against Werder Bremen, which Frankfurt lost 2–1, Salcedo suffered a high ankle sprain, meaning he would be ruled out of action for an undetermined amount of time. On 2 December, he reappeared as an unused substitute in Frankfurt's 2–1 loss to Wolfsburg. Six days later, he made his return to the starting eleven in Frankfurt's 1–0 loss to Hertha Berlin.


title: Carlos Salcedo

text: On 22 January 2019, amidst much speculation, Tigres UANL announced via social media the signing of Salcedo to a four-year contract, being handed the number 3 which had previously been worn by Juninho, who had retired at the conclusion of the 2018 Apertura. He had cited family issues as the main reason for returning to Mexico. Salcedo also revealed that he did not return to C.D. Guadalajara because the team was only looking to acquire him on loan from Frankfurt, an offer which was declined by the German side. Two weeks after being officially presented with Tigres, Salcedo made his Liga MX debut in a 2–0 victory against Veracruz.


title: Carlos Salcedo

text: On 12 March, in the second leg of the 2019 CONCACAF Champions League quarter-finals against MLS side Houston Dynamo, Salcedo scored his first goal with Tigres in a 1–0 victory. Four days later, he scored his first league goal with Tigres in a 4–1 victory over Querétaro. Despite Tigres finishing runners-up in the CONCACAF Champions League Finals to city rivals C.F. Monterrey, Salcedo was included in the competition's Best XI. The following month, on 26 May, Salcedo won the Clausura championship with Tigres after defeating León 1–0 on aggregate in the finals.


title: Carlos Salcedo

text: On 22 December 2020, Tigres won the CONCACAF Champions League after defeating MLS side Los Angeles FC 2–1.


title: Carlos Salcedo

text: On 31 January 2022, Salcedo returned to MLS, signing with Toronto FC as a Designated Player. He made his debut on 26 February in the season opener against FC Dallas. On 12 July 2022, Toronto and Salcedo mutually agreed to terminate his contract to allow him to move back to Mexico for family reasons.


title: Carlos Salcedo

text: Shortly after leaving Toronto FC, Salcedo returned to Liga MX, signing with Juárez. He made his debut on 22 July against Necaxa.


title: Carlos Salcedo

text: Salcedo was called up by Raúl Gutiérrez to participate in the 2014 Central American and Caribbean Games. He went on to appear in four matches as Mexico won the tournament.


title: Carlos Salcedo

text: On 18 September 2015, Salcedo was once again selected by coach Raúl Gutiérrez to play in the CONCACAF Olympic Qualifying Championship. Chosen as team captain for the competition, he appeared in four matches, winning the tournament and a berth to the Summer Olympics.


title: Carlos Salcedo

text: On 7 July 2016, Salcedo was named in Mexico's 23-man squad for the Summer Olympics in Rio de Janeiro. He appeared in all three group stage matches, scoring the fourth goal in a 5–1 defeat of Fiji, though Mexico failed to make it out of the group after finishing in third.


title: Carlos Salcedo

text: Salcedo was called up by Miguel Herrera to participate with the senior national team and on 15 April 2015, he made his debut in a friendly game against the United States, losing 0–2. He was included in the final roster to participate in that year's Copa América. He only made one appearance, on 15 June, coming on as a substitute in the 71st minute for Adrián Aldrete in a 3–3 draw against host-nation Chile.


title: Carlos Salcedo

text: On 8 June 2017, Salcedo was included by Juan Carlos Osorio to be Mexico's 23-man squad for the FIFA Confederations Cup in Russia. On 21 June, during Mexico's second group stage match against New Zealand, Salcedo was taken off during the first half after sustaining a shoulder injury following a collision with striker Chris Wood. He was subsequently ruled out for the rest of the tournament.


title: Carlos Salcedo

text: On 27 March 2018, during a friendly match against Croatia he would pick up a fractured left collarbone injury, putting in risk a call up for the FIFA World Cup. Salcedo was subsequently named in the final 23-man squad for the World Cup. He played in all group stage matches, including in the round-of-16 loss against Brazil. Following Mexico's elimination, Salcedo pondered his future with the national team, citing personal issues. He was eventually called up to participate in September friendlies by interim manager Ricardo Ferretti, but withdrew due to a high ankle sprain injury.


title: Carlos Salcedo

text: On 6 June 2019, Salcedo was called up by coach Gerardo Martino to participate in the Gold Cup. In the quarter-final match against Costa Rica, as the match was sent to a penalty shoot-out following a 1–1 tie, he scored Mexico's winning penalty before Mexico goalkeeper Guillermo Ochoa blocked the subsequent Costa Rica shot. As Mexico went on to win the tournament after defeating the United States 1–0 in the final, he was named in the competition's Best XI.


title: Carlos Salcedo

text: On 30 September 2020, he appeared as captain in a friendly match against Guatemala, winning 3–0. On 14 November, Salcedo scored his first goal in a friendly match against South Korea, winning 3–2.


title: Carlos Salcedo

text: A natural center-back, Salcedo has been deployed as a full-back: on the right side while playing for the Mexico national team and on the left when he used to play for Real Salt Lake. He is known as "a good passer and as a concentrated player who likes to play long balls, he is known for his well timed slide tackles and his strength in the back line, his abilities to win most of the aerial duels makes him a complete defender." He has also been described as "tall, strong, physically imposing and quick on the ball. He has superb slide tackling skills and is willing to throw his body into danger if it means stopping an opponents attack." He is commonly known by his nickname "Titan", as a result of his imposing physical presence and his speedy recoveries from injuries, as well as being able to play through them. In an interview with Tom Marshall from Goal.com, Salcedo stated that his early move to the MLS would help develop his playing style, arguing "that MLS is generally more physical than in Mexico, but that learning to combat a more direct style complements the technique and comfort on the ball that was drilled into him, first at [Guadalajara] and later with Tigres."


title: Carlos Salcedo

text: His father, Carlos Salcedo Snr, played for Atlas F.C. in Mexico, his great-grandfather had played for C.D. Guadalajara and been a league winner in Mexico. His great-uncle, Hugo Salcedo, played Soccer for the U.S. at the 1972 Olympic Games. His son and Carlos’s first-cousin, once removed, Jorge Salcedo played for four teams in MLS between 1996-2000, and was capped by the United States national soccer team.


title: French Alps

text: The French Alps are the portions of the Alps mountain range that stand within France, located in the Auvergne-Rhône-Alpes and Provence-Alpes-Côte d'Azur regions. While some of the ranges of the French Alps are entirely in France, others, such as the Mont Blanc massif, are shared with Switzerland and Italy.


title: French Alps

text: At , Mont Blanc (Italian: "Monte Bianco"), on the France–Italy border, is the highest mountain in the Alps, and the highest Western European mountain.


title: French Alps

text: Notable towns in the French Alps include Grenoble, Chamonix, Annecy, Chambéry, Évian-les-Bains and Albertville.


title: French Alps

text: A range of winter and summer activities are available in the French Alps. In the winter, these include skiing and snowboarding as well as alternatives such as snowshoeing, sledging. There is a range of other activities that happen such as gliding which most happens during the summer months. Summer activities include hiking, mountaineering, biking and rock climbing.


title: Székely Land

text: The Székely Land or Szeklerland (, ; and sometimes ; ; ) is a historic and ethnographic area in Romania, inhabited mainly by Székelys, a subgroup of Hungarians. Its cultural centre is the city of Târgu Mureș (Marosvásárhely), the largest settlement in the region.


title: Székely Land

text: Székelys (or Szeklers) live in the valleys and hills of the Eastern Carpathian Mountains, corresponding mostly to the present-day Harghita, Covasna, and parts of Mureș counties in Romania.


title: Székely Land

text: Originally, the name "Székely Land" denoted the territories of a number of autonomous Székely seats within Transylvania. The self-governing Székely seats had their own administrative system, and existed as legal entities from medieval times until the 1870s. The privileges of the Székely and Saxon seats were abolished and seats were replaced with counties in 1876.


title: Székely Land

text: Along with Transylvania and eastern parts of Hungary proper, the Székely Land became a part of Romania in 1920, in accordance with the Treaty of Trianon. In August 1940, as a consequence of the Second Vienna Award, northern territories of Transylvania, including the Székely Land, were returned to Hungary. Northern Transylvania came under the control of Soviet and Romanian forces in 1944, and were confirmed as part of Romania by the Paris Peace Treaties signed after World War II.


title: Székely Land

text: Under the name Magyar Autonomous Region, with Târgu-Mureș as capital, parts of the Székely Land enjoyed a certain level of autonomy between 8 September 1952 and 16 February 1968.


title: Székely Land

text: There are territorial autonomy initiatives with the aim to obtain self-governance for this region within Romania.


title: Székely Land

text: The exact territory of the present-day Székely Land is disputed. The boundaries of the historical Székely seats and the present-day administrative divisions of Romania are dissimilar. According to Minahan its territory is an estimated . The autonomy proposal of the Szekler National Council consists of about 13,000 km. This size is close to the extent of the historical Székely Land. However, it does not contain the region of Aranyos Seat. The UDMR's autonomy project covers a slightly bigger territory. It includes the whole territories of Mureș, Harghita, and Covasna counties.


title: Székely Land

text: Transylvania was populated by Thracian peoples in the First Iron Age. The area received a large influx of Scythians from the East in the first half of the first millennium BC. The Celts appeared in Transylvania in the La Tène period (c. 4th century BC).


title: Székely Land

text: Dacian culture presence in southeastern Transylvania is marked by discoveries such as the flagship hoard Sâncrăieni (Harghita county) or Dacian fortresses in Covasna county (Cetatea Zânelor) or Jigodin (Harghita county).


title: Székely Land

text: Dacian Kingdom led by Decebal was taken after two wars, in 106 AD by the Roman Empire under the emperor Trajan, who began organizing the new Roman province of Dacia. Southeastern Transylvania was included in the provinces of Dacia Porolissensis, Dacia Apulensis and Meuse and fortified with numerous camps such as those at Inlăceni ( Praetoria Augusta) and Sânpaul (Harghita county) Breţcu (Angustia) and Oltenia (Covasna county) or Brâncoveneşti and Călugăreni (Mureș county).


title: Székely Land

text: After the fall of Roman Dacia, the present-day territory of the Székely Land became part of the Thervingi kingdom ""Gutthiuda"". The migration of the Huns from the east pressured most of the German tribes to leave. In the Battle of Nedao the East Germanic Gepids defeated the Huns and founded Gepidia in the territory of present-day Transylvania. This marked the end of the Hunnic Empire.


title: Székely Land

text: The territory of the Székely Land was part of the Avar Khaganate. During this period, Avar and Slavic groups migrated into Transylvania. From around 900 to 1526 the area was under the direct control of the Hungarian state. The Székelys presumably settled in Transylvania in the 12th century from present day Bihar and Bihor counties.


title: Székely Land

text: Ancient Hungarian legends suggest a connection between the Székelys and Attila's Huns. The origin of the Székely people is still debated. The Székely seats were the traditional self-governing territorial units of the Transylvanian Székelys during medieval times. (Saxons were also organised in seats.) The Seats were not part of the traditional Hungarian county system, and their inhabitants enjoyed a higher level of freedom (especially until the 18th century) than those living in the counties.


title: Székely Land

text: From the 12th and 13th centuries, the Székely Land enjoyed a considerable but varying amount of autonomy, first as a part of the Kingdom of Hungary, then inside the Principality of Transylvania. The autonomy was largely due to the military service the Székely provided until the beginning of the 18th century. The medieval Székely Land was an alliance of the seven autonomous Székely seats of "Udvarhely", "Csík", "Maros", "Sepsi", "Kézdi", "Orbai" and "Aranyos". The number of seats later decreased to five, when "Sepsi", "Kézdi" and "Orbai" seats were united into one territorial unit called "Háromszék" (literally "Three seats").


title: Székely Land

text: The main seat was Udvarhely seat, which was also called the Principal seat () At Székelyudvarhely (Odorheiu Secuiesc) were held many national assemblies of the Székelys A known exception is the 1554 assembly, which took place at Marosvásárhely (Târgu Mureș)


title: Székely Land

text: Due to the Ottoman conquest Transylvania became a semi-independent polity. From the end of the 17th century, Transylvania became part of the Habsburg monarchy (later Austrian Empire), and governed by imperial governors. In 1867, as a result of the Austro-Hungarian Compromise, Transylvania become an integral part of the Kingdom of Hungary, within Austria-Hungary.


title: Székely Land

text: In 1876, a general administrative reform abolished all the autonomous areas in the Kingdom of Hungary and created a unified system of counties. As a result, the autonomy of the Székely Land came to an end as well. Four counties were created in its place: Udvarhely, Háromszék, Csík, and Maros-Torda. (Only half of the territory of Maros-Torda originally belonged to the Székely Land.) The isolated Aranyosszék became a district of Torda-Aranyos county.


title: Székely Land

text: In December 1918, in the wake of the First World War, Romanian delegates from throughout Transylvania voted to join the Kingdom of Romania. There was an attempt in Udvarhely to found a "Székely republic" on 9 January 1919; however, its creation was unsuccessful. In 1920, by the Treaty of Trianon, Transylvania along with further territories was officially ceded to the Kingdom of Romania. The Romanian language officially replaced Hungarian in the Székely Land, but Székely county boundaries were preserved, and Székely districts were able to elect their own officials at local level and to preserve Hungarian-language education.


title: Székely Land

text: After 1930, the Romanian authorities began to Romanianize the Hungarian population of the Székely Land, with the presence of minorities in political life being repressed. The election of Hungarians was consistently nullified. The place-names were subjected to Romanianization. The minority languages were excised from official life and the local authorities were mostly led by appointed ethnic Romanians.


title: Székely Land

text: In 1940, as a result of the Second Vienna Award, Northern Transylvania became part of Hungary again; this territory included most of the historical Székely areas. Hungarian authorities subsequently restored the pre-Trianon structure with slight modifications.


title: Székely Land

text: Ion Gigurtu's antisemitic laws, the Romanian version of Nuremberg Laws, were replaced by Hungarian ones. The Jews of the Székely Land were subjected to particularly harsh treatment. These individuals had their citizenship status reviewed, many of them being detained. In Csíkszereda ("Miercurea Ciuc"), dozens of families were rounded up and expelled. The men in the area were drafted into forced labor battalions. For example, 1,200 Jewish males of Marosvásárhely ("Târgu Mureș") were conscripted between 1941 and 1944; over half died in Ukraine, Poland and Hungary.


title: Székely Land

text: However, despite discrimination and many casualties, most of the community lived in relative safety until the March 1944 occupation of Hungary by Nazi Germany. A conference devoted to the concentration of Jews in the Székely Land was held on 28 April 1944; it covered the counties of Csík, Háromszék, Maros-Torda and Udvarhely. The area's Jews were ghettoized in Szászrégen ("Reghin"), Sepsiszentgyörgy ("Sfântu Gheorghe") and Marosvásárhely. Roundups began on 3 May 1944 and were completed within a week. The Hungarian authorities actively participated in the crimes of the Nazis. The Jews ghettoized at Sepsiszentgyörgy were later sent to Szászrégen, whence on 4 June 1944, 3,149 were boarded on a train bound for the Auschwitz concentration camp. Three transports left Marosvásáhely for Auschwitz: on 27 May, 30 May and 8 June 1944; altogether, they carried 7,549 Jews.


title: Székely Land

text: On 12 September 1944, the Second Vienna Award was voided by the Allied Commission through the Armistice Agreement with Romania, and the Romanian-Soviet forces seized the area in Autumn 1944; however, the Romanian administration was expelled from these territories in October due to the activities of the Romanian paramilitary groups created in the area to avenge the atrocities committed by the Hungarians against the Romanians during the Hungarian rule in Northern Transylvania. For instance, the so-called "Iuliu Maniu Guards" terrorized the Székely villages, butchered the local Hungarians by axe and hatchet and operated a death camp in Feldioara. This paramilitary group was described as ""a band of terrorist-chauvinistic criminals"" by the Soviets. The USSR let the Romanian authorities back to the area in March 1945, and the Paris Peace Treaties officially returned Northern Transylvania to Romania.


title: Székely Land

text: Following the Northern Transylvania's return to Romania after World War II, a Magyar Autonomous Region was created in 1952 under the Soviets' pressure, which encompassed most of the land inhabited by the Székelys. In 1960, the region was renamed to Mureș-Magyar Autonomous Region. It was abolished in 1968, when Romania, following an administrative reform, returned to its traditional local administrative system based on counties. Roughly speaking, present-day Harghita County encompasses the former Udvarhely and Csík, the latter including Gyergyószék; Covasna County covers more or less the territory of the former Háromszék; and what was once Maros-Torda is mostly part of present-day Mureș County. The former Aranyosszék is today divided between Cluj and Alba counties.


title: Székely Land

text: Nicolae Ceaușescu came to power in 1965. For the next couple of decades, due to the Romanianization efforts, a large number of ethnic Romanians settled in the Székely Land. Those Székely Hungarians who possessed degrees were subjected to resettlement.


title: Székely Land

text: In March 1990, the city of Târgu Mureș witnessed violent clashes between ethnic Romanian and Hungarian groups.


title: Székely Land

text: After the fall of communism, many hoped that the former Magyar Autonomous Region, abolished by Nicolae Ceauşescu's regime, would soon be restored. This did not happen; however, there are Székely autonomy initiatives and further efforts from Székely organisations to reach a higher level of self-governance for the Székely Land within Romania.


title: Székely Land

text: On 4 June 2005, the Civic Forum of the Romanians of Covasna, Harghita and Mureș was founded in Miercurea Ciuc. It is an organization aimed at organizing the ethnic Romanian population in the counties that compose Székely Land.


title: Székely Land

text: On 2 February 2009, Romanian President Traian Băsescu met the Hungarian President László Sólyom in Budapest and discussed the issues of minority rights and regional autonomy. Băsescu stated "The Hungarian minority will never be given territorial autonomy."


title: Székely Land

text: In 2014, the UDMR and the Hungarian Civic Party had a joint autonomy proposal for the Székely Land, but the Szekler National Council also possessed its own suggestion.


title: Székely Land

text: In 2016, Hans G. Klemm, the United States Ambassador to Romania, together with other local officials, were pictured with a Székely flag during his visit to the Székely Land. The photo was posted by the mayor of Sfântu Gheorghe on Facebook. The reactions of the politicians in Bucharest were turbulent. In a response Klemm affirmed that the only two flags that are important to him, as a diplomat, are the U.S. and the Romanian ones.


title: Székely Land

text: Article 1 of the Romanian Constitution defines the country as a "sovereign, independent, unitary and indivisible national state." It has often been argued that, as a result of this provision, any ethnic-based territorial autonomy, including that of the Székely Land, would be unconstitutional.


title: Székely Land

text: The Supreme Council of National Defence of Romania declared that an autonomy of the so-called Székely Land would be unconstitutional.


title: Székely Land

text: In 2002 the estimated ethnic composition of the Székely Land (Mureș, Covasna and Harghita counties) consisted of Hungarians (61%), Romanians (33%), Germans (3%) and Roma (3%). The area forms a Hungarian ethnic enclave within present-day Romania. Locals refer this situation as ""Everybody speaks Hungarian," "here you have to speak Romanian with police and public officials"."


title: Székely Land

text: The population of the historical Székely Land (according to the 2002 census) is 809,000, 612,043 of them Hungarians, accounting for 75.65% of the total. The Hungarians represent 59% of the populations of Harghita, Covasna and Mureș counties. The percentage of Hungarians is higher in Harghita and Covasna (84.8% and 73.58% respectively), and lower in Mureș County, not all of which falls inside the traditional region (37.82%).


title: Székely Land

text: According to the 2011 official census, 609,033 Hungarians (56.8%) live in the counties of Covasna, Harghita and Mureș (out of a total population of 1,071,890 inhabitants). In Mureș county the Romanians are the most numerous (52.6%), while in the counties of Covasna and Harghita, the Hungarians make up the majority (71.6% and 82.9%). The 2011 census compared to the data of the previous census (2002) also shows that the Romanian ethnic ratio in the Székely Land has been decreasing (due to emigration).


title: Székely Land

text: Târgu Mureș is the home for the largest community of Hungarians in Romania (57,532 in 2011), but the town itself has a Romanian majority (66,943 out of 127,849 inhabitants).


title: Székely Land

text: Important centers of the Székely Land are Târgu-Mureș ("Marosvásárhely"), Miercurea Ciuc ("Csíkszereda"), Sfântu Gheorghe ("Sepsiszentgyörgy"), and Odorheiu Secuiesc ("Székelyudvarhely").


title: Székely Land

text: The Székely ice hockey team Sport Club of Csíkszereda, with mainly home trained, local players (Székelys), plays simultaneously in the Erste League (Hungarian League) and in the Romanian Ice Hockey Championship. Starting with the 2010/2011 season, the Sport Club ice hockey team participated at the championships under the name HSC Csíkszereda and that year it won its first Erste League title as well.


title: Székely Land

text: The Romanian Championship (fifteen times winner): 1949, 1952, 1957, 1960, 1963, 1997, 2000, 2004, 2007, 2008, 2009, 2010, 2011, 2012, 2013.


title: Székely Land

text: The majority of the Romanian men's national ice hockey team consist of Székely players. The national team are ranked 28th in the 2010 IIHF World Rankings and currently compete in Division IIA.


title: Social research

text: Social research is a research conducted by social scientists following a systematic plan. Social research methodologies can be classified as quantitative and qualitative.


title: Social research

text: While methods may be classified as quantitative or qualitative, most methods contain elements of both. For example, qualitative data analysis often involves a fairly structured approach to coding the raw data into systematic information, and quantifying intercoder reliability. Thus, there is often a more complex relationship between "qualitative" and "quantitative" approaches than would be suggested by drawing a simple distinction between them.


title: Social research

text: Social scientists employ a range of methods in order to analyse a vast breadth of social phenomena: from census survey data derived from millions of individuals, to the in-depth analysis of a single agent's social experiences; from monitoring what is happening on contemporary streets, to the investigation of ancient historical documents. Methods rooted in classical sociology and statistics have formed the basis for research in other disciplines, such as political science, media studies, program evaluation and market research.


title: Social research

text: Social scientists are divided into camps of support for particular research techniques. These disputes relate to the historical core of social theory (positivism and antipositivism; structure and agency). While very different in many aspects, both qualitative and quantitative approaches involve a systematic interaction between theory and data. The choice of method often depends largely on what the researcher intends to investigate. For example, a researcher concerned with drawing a statistical generalization across an entire population may administer a survey questionnaire to a representative sample population. By contrast, a researcher who seeks full contextual understanding of an individuals' social actions may choose ethnographic participant observation or open-ended interviews. Studies will commonly combine, or "triangulate", quantitative "and" qualitative methods as part of a multi-strategy design.


title: Social research

text: Typically a population is very large, making a census or a complete enumeration of all the values in that population infeasible. A sample thus forms a manageable subset of a population. In positivist research, statistics derived from a sample are analysed in order to draw inferences regarding the population as a whole. The process of collecting information from a sample is referred to as "sampling". Sampling methods may be either random (random sampling, systematic sampling, stratified sampling, cluster sampling) or non-random/nonprobability (convenience sampling, purposive sampling, snowball sampling). The most common reason for sampling is to obtain information about a population. Sampling is quicker and cheaper than a complete census of a population.


title: Social research

text: Social research is based on logic and empirical observations. Charles C. Ragin writes in his "Constructing Social Research" book that "Social research involved the interaction between ideas and evidence. Ideas help social researchers make sense of evidence, and researchers use evidence to extend, revise and test ideas." Social research thus attempts to create or validate theories through data collection and data analysis, and its goal is exploration, description, explanation, and prediction. It should never lead or be mistaken with philosophy or belief. Social research aims to find social patterns of regularity in social life and usually deals with social groups (aggregates of individuals), not individuals themselves (although science of psychology is an exception here). Research can also be divided into pure research and applied research. Pure research has no application on real life, whereas applied research attempts to influence the real world.


title: Social research

text: There are no laws in social science that parallel the laws in natural science. A law in social science is a universal generalization about a class of facts. A fact is an observed phenomenon, and observation means it has been seen, heard or otherwise experienced by researcher. A theory is a systematic explanation for the observations that relate to a particular aspect of social life. Concepts are the basic building blocks of theory and are abstract elements representing classes of phenomena. Axioms or postulates are basic assertions assumed to be true. Propositions are conclusions drawn about the relationships among concepts, based on analysis of axioms. Hypotheses are specified expectations about empirical reality derived from propositions. Social research involves testing these hypotheses to see if they are true.


title: Social research

text: Social research involves creating a theory, operationalization (measurement of variables) and observation (actual collection of data to test hypothesized relationship). Social theories are written in the language of variables, in other words, theories describe logical relationships between variables. Variables are logical sets of attributes, with people being the "carriers" of those variables (for example, gender can be a variable with two attributes: male and female). Variables are also divided into independent variables (data) that influences the dependent variables (which scientists are trying to explain). For example, in a study of how different dosages of a drug are related to the severity of symptoms of a disease, a measure of the severity of the symptoms of the disease is a dependent variable and the administration of the drug in specified doses is the independent variable. Researchers will compare the different values of the dependent variable (severity of the symptoms) and attempt to draw conclusions.


title: Social research

text: When social scientists speak of "good research" the guidelines refer to how the science is mentioned and understood. It does not refer to how what the results are but how they are figured. Glenn Firebaugh summarizes the principles for good research in his book "Seven Rules for Social Research". The first rule is that "There should be the possibility of surprise in social research." As Firebaugh (p. 1) elaborates: "Rule 1 is intended to warn that you don't want to be blinded by preconceived ideas so that you fail to look for contrary evidence, or you fail to recognize contrary evidence when you do encounter it, or you recognize contrary evidence but suppress it and refuse to accept your findings for what they appear to say."


title: Social research

text: In addition, good research will "look for differences that make a difference" (Rule 2) and "build in reality checks" (Rule 3). Rule 4 advises researchers to replicate, that is, "to see if identical analyses yield similar results for different samples of people" (p. 90). The next two rules urge researchers to "compare like with like" (Rule 5) and to "study change" (Rule 6); these two rules are especially important when researchers want to estimate the effect of one variable on another (e.g. how much does college education actually matter for wages?). The final rule, "Let method be the servant, not the master," reminds researchers that methods are the means, not the end, of social research; it is critical from the outset to fit the research design to the research issue, rather than the other way around.


title: Social research

text: Explanations in social theories can be idiographic or nomothetic. An idiographic approach to an explanation is one where the scientists seek to exhaust the idiosyncratic causes of a particular condition or event, i.e. by trying to provide all possible explanations of a particular case. Nomothetic explanations tend to be more general with scientists trying to identify a few causal factors that impact a wide class of conditions or events. For example, when dealing with the problem of how people choose a job, idiographic explanation would be to list all possible reasons why a given person (or group) chooses a given job, while nomothetic explanation would try to find factors that determine why job applicants in general choose a given job.


title: Social research

text: Research in science and in social science is a long, slow and difficult process that sometimes produces false results because of methodological weaknesses and in rare cases because of fraud, so that reliance on any one study is inadvisable.


title: Social research

text: The ethics of social research are shared with those of medical research. In the United States, these are formalized by the Belmont report as:


title: Social research

text: The principle of respect for persons holds that (a) individuals should be respected as autonomous agents capable of making their own decisions, and that (b) subjects with diminished autonomy deserve special considerations. A cornerstone of this principle is the use of informed consent.


title: Social research

text: The principle of beneficence holds that (a) the subjects of research should be protected from harm, and, (b) the research should bring tangible benefits to society. By this definition, research with no scientific merit is automatically considered unethical.


title: Social research

text: The principle of justice states the benefits of research should be distributed fairly. The definition of fairness used is case-dependent, varying between "(1) to each person an equal share, (2) to each person according to individual need, (3) to each person according to individual effort, (4) to each person according to societal contribution, and (5) to each person according to merit."


title: Social research

text: The origin of the survey can be traced back at least early as the Domesday Book in 1086, while some scholars pinpoint the origin of demography to 1663 with the publication of John Graunt's "Natural and Political Observations upon the Bills of Mortality". Social research began most intentionally, however, with the positivist philosophy of science in the early 19th century.


title: Social research

text: Statistical sociological research, and indeed the formal academic discipline of sociology, began with the work of Émile Durkheim (1858–1917). While Durkheim rejected much of the detail of Auguste Comte's philosophy, he retained and refined its method, maintaining that the social sciences are a logical continuation of the natural ones into the realm of human activity, and insisting that they may retain the same objectivity, rationalism, and approach to causality. Durkheim set up the first European department of sociology at the University of Bordeaux in 1895, publishing his "Rules of the Sociological Method" (1895). In this text he argued: main goal is to extend scientific rationalism to human conduct. ... What has been called our positivism is but a consequence of this rationalism."


title: Social research

text: Durkheim's seminal monograph, "Suicide" (1897), a case study of suicide rates among Catholic and Protestant populations, distinguished sociological analysis from psychology or philosophy. By carefully examining suicide statistics in different police districts, he attempted to demonstrate that Catholic communities have a lower suicide rate than that of Protestants, something he attributed to social (as opposed to individual or psychological) causes. He developed the notion of objective "suis generis" "social facts" to delineate a unique empirical object for the science of sociology to study. Through such studies he posited that sociology would be able to determine whether any given society is "healthy" or "pathological", and seek social reform to negate organic breakdown or "social anomie". For Durkheim, sociology could be described as the "science of institutions, their genesis and their functioning".


title: Social research

text: In the early 20th century innovation in survey methodology were developed that are still dominant. In 1928, the psychologist Louis Leon Thurstone developed a method to select and score multiple items with which to measure complex ideas, such as attitudes towards religion. In 1932, the psychologist Rensis Likert developed the Likert scale where participants rate their agreement with statement using five options from totally disagree to totally agree. Likert like scales remain the most frequently used items in survey.


title: Social research

text: In the mid-20th century there was a general—but not universal—trend for American sociology to be more scientific in nature, due to the prominence at that time of action theory and other system-theoretical approaches. Robert K. Merton released his "Social Theory and Social Structure" (1949). By the turn of the 1960s, sociological research was increasingly employed as a tool by governments and businesses worldwide. Sociologists developed new types of quantitative and qualitative research methods. Paul Lazarsfeld founded Columbia University's Bureau of Applied Social Research, where he exerted a tremendous influence over the techniques and the organization of social research. His many contributions to sociological method have earned him the title of the "founder of modern empirical sociology". Lazarsfeld made great strides in statistical survey analysis, panel methods, latent structure analysis, and contextual analysis. Many of his ideas have been so influential as to now be considered self-evident.


title: Honey Lacuna

text: Maria Sheilah Honrado Lacuna–Pangan (born May 6, 1965), publicly known as Honey Lacuna, is a Filipino physician and politician who is currently serving as the Mayor of Manila since 2022.


title: Honey Lacuna

text: Lacuna-Pangan was born to Danilo "Danny" Lacuna, a lawyer who would later serve as a city councilor (1967–1975) and vice mayor of Manila (1970–1971; 1988–1992; 1998–2007), and Melanie Honrado, a former Philippine National Bank (PNB) executive. She earned a biology degree at the University of Santo Tomas, earned a Doctor of Medicine degree from De La Salle University – Emilio Aguinaldo College, passed the physician board examination in 1992, and completed her residency training in dermatology at the Ospital ng Maynila Medical Center. Soon after taking her residency training for dermatology at the Ospital ng Maynila Medical Center, she eventually became a fellow of the Philippine Dermatological Society.


title: Honey Lacuna

text: A general practitioner with specialization in dermatology by profession, Lacuna worked as a resident physician of the dermatology department of Ospital ng Maynila Medical Center from 1992 to 1995 and as the public health center physician under the Manila Health Department from 1995 to 2004. As the latter, she was assigned at the Bacood Health Center in Santa Mesa and later at the Tondo Health Center in Tondo. Her father, then vice mayor Danny Lacuna, then tasked her to head the medical team of his office's regular medical and dental mission conducted every week in various depressed communities in Manila.


title: Honey Lacuna

text: She served the director of the Social Welfare Department of the city from 2013 to 2015. Even as a politician, Lacuna continued her door-to-door visit to patients that she has been doing since before entering politics.


title: Honey Lacuna

text: Lacuna then entered politics when she substituted a candidate for councilor in the 4th district of Manila who withdrew from the race ahead of the 2004 city elections. She ran under the ticket of her father, who was the running mate of former mayor Mel Lopez of Koalisyon ng Nagkakaisang Pilipino. She then won, serving as a Manila city councilor from the 4th district for three consecutive terms from 2004 to 2013. As councilor, she served in the minority whip from 2004 to 2007, chairperson of the Committee on Education, a member of 38 committees, and majority floor leader, the first woman to be named so. She also authored, among others, the following:


title: Honey Lacuna

text: In the 2016 city election, she was chosen as the running mate of incumbent mayor Joseph Estrada, who was seeking re-election under Pwersa ng Masang Pilipino (PMP); she then won the vice mayoralty race. She became the first woman to be elected vice mayor since the post became an elective position. She was then reelected in 2019, this time as the running mate of her predecessor Francisco "Isko Moreno" Domagoso, who was running for mayor under Asenso Manileño. During the COVID-19 pandemic, she stood as a point person for Moreno in coordinating with the hospital directors of Manila, applying her expertise as a medical doctor. In 2021, she joined Aksyon Demokratiko and was named as the party's Vice-President for Internal Affairs and National Executive Board Member.


title: Honey Lacuna

text: With Isko Moreno running for president in 2022, Lacuna was nominated by Asenso Manileño to run for mayor in 2022 to succeed him, with Manila's 3rd district representative Yul Servo Nieto as her running mate and vice mayoralty candidate. She won the race by a huge margin over her closest rival, Atty. Alex Lopez, making her the first-ever female to be elected mayor of Manila in 450 years. She was inaugurated before outgoing mayor Moreno on June 29, 2022 at the Manila Cathedral, but only officially started her term on the next day, succeeding him. As mayor, she vowed to prioritize health care and expand Moreno's programs.


title: Honey Lacuna

text: On August 5, 2022, Lacuna was conferred with a degree of Doctor of Public Administration, "honoris causa" by the Pamantasan ng Lungsod ng Maynila.


title: Honey Lacuna

text: Lacuna is married to Arnold "Poks" Martin Pangan, a fellow physician and registered social worker who is the incumbent director of the Manila Health Department and a 2013 candidate for Manila councilor from the 4th district. They have one daughter.


title: Honey Lacuna

text: Lacuna was diagnosed with COVID-19 in August 2021. She later recovered from the disease in the same month.


title: Ghaggar-Hakra River

text: The Ghaggar-Hakra River is an intermittent river in India and Pakistan that flows only during the monsoon season. The river is known as Ghaggar in India, before the Ottu barrage, and as the Hakra in Pakistan, downstream of the barrage, ending in the Thar Desert. In pre-Harappan times the Ghaggar was a tributary of the Sutlej. It is still connected to this paleochannel of the Sutlej, and possibly the Yamuna, which ended in the Nara River, presently a delta channel of the Indus River joining the sea via Sir Creek.


title: Ghaggar-Hakra River

text: The Sutlej changed its course about 8,000-10,000 years ago, leaving the Ghaggar-Hakra as a system of monsoon-fed rivers terminating in the Thar Desert. The Indus Valley civilisation prospered when the monsoons that fed the rivers diminished around 5,000 years ago, and a large number of sites from the Mature Indus Valley Civilisation (2600-1900 BCE) are found along the middle course of the (dried-up) Hakra in Pakistan. Around 4,000 years ago, the Indus Valley Civilisation declined when the monsoons further diminished, and the Ghaggar-Hakra dried up, becoming a small seasonal river.


title: Ghaggar-Hakra River

text: Nineteenth and early 20th century scholars, but also some more recent authors, have suggested that the Ghaggar-Hakra might be the defunct remains of the Sarasvati River mentioned in the Rig Veda, fed by Himalayan-fed rivers, despite the fact that the Ghaggar-Hakra had dried up by that time.


title: Ghaggar-Hakra River

text: The basin consists of two parts, Khadir and Bangar. "Bangar" are the higher banks that are not flooded in rainy season, while "khadar" refers to the lower flood-prone area.


title: Ghaggar-Hakra River

text: The Ghaggar is an intermittent river in India, flowing during the monsoon rains. It originates in the village of Dagshai in the Shivalik Hills of Himachal Pradesh at an elevation of above mean sea level and flows through Punjab and Haryana states into Rajasthan; just southwest of Sirsa, Haryana and by the side of Talwara Lake in Rajasthan.


title: Ghaggar-Hakra River

text: The Kaushalya river is a tributary of Ghaggar river on the left side of Ghaggar-Hakra, it flows in the Panchkula district of Haryana state of India and confluences with Ghaggar river near Pinjore just downstream of Kaushalya Dam.


title: Ghaggar-Hakra River

text: The Hakra is the dried-out channel of a river near Fort Abbas City in Pakistan that is the continuation of the Ghaggar River in India. The Hakra-channel is connected to paleochannels of the Sutlej and the Yamuna, which ended in the Nara River, a delta channel of the Indus River joining the sea via Sir Creek. The Sutlej changed its course about 8,000-10,000 years ago, leaving the Ghaggar-Hakra as a system of monsoon-fed rivers terminating in the Thar Desert.


title: Ghaggar-Hakra River

text: This Sutlej/Yamuna paleochannel streamed through Sindh, and its sign can be found in Sindh areas such as Khairpur, Nawabshah, Sanghar and Tharparkar.


title: Ghaggar-Hakra River

text: A large number of sites from the Mature Indus Valley civilisation (2600-1900 BCE) are found along the middle course of the (dried-up) Hakra in Pakistan. IVC-sites have not been found further south than the middle of Bahawalpur district, and it has been assumed that the Hakra ended there in a series of terminal lakes.


title: Ghaggar-Hakra River

text: While there is general agreement that the river courses in the Indus Basin have frequently changed course, the exact sequence of these changes and their dating have been problematic.


title: Ghaggar-Hakra River

text: Older publications have suggested that the Sutlej and the Yamuna drained into the Hakra well into Mature Harappan times, providing ample volume to the supply provided by the monsoon-fed Ghaggar. The Sutlej and Yamuna then changed course between 2500 BCE and 1900 BCE, due to either tectonic events or "slightly altered gradients on the extremely flat plains," resulting in the drying-up of the Hakra in the Thar Desert. More recent publications have shown that the Sutlej and the Yamuna shifted course well before Harappan times, leaving the monsoon-fed Ghaggar-Hakra which dried-up during late Harappan times.


title: Ghaggar-Hakra River

text: The paleo-channel of the Sutlej was active until the end of the Ice Age, some 10,000-8,000 years ago, emptying into the Rann of Kutch via the Nara river.


title: Ghaggar-Hakra River

text: Clift "et al". (2012), using dating of zircon sand grains, have shown that subsurface river channels near the Indus Valley civilisation sites in Cholistan immediately below the dry Ghaggar-Hakra bed show sediment affinity with the Beas River in the western sites and the Sutlej and the Yamuna in the eastern ones, suggesting that the Yamuna itself, or a channel of the Yamuna, along with a channel of the Sutlej may have flowed west some time between 47,000 BCE and 10,000 BCE, well before the beginnings of Indus civilization.


title: Ghaggar-Hakra River

text: Analysis of sand grains using optically stimulated luminescence by Ajit Singh and others in 2017 indicated that the suggested paleochannel of the Ghaggar-Hakra is actually a former course of the Sutlej, which diverted to its present course before the development of the Harappan Civilisation. The abandonment of this older course by the Sutlej started 15,000 years ago, and was complete by 8,000 years ago. Ajit Singh et al. conclude that the urban populations settled not along a perennial river, but a monsoon-fed seasonal river that was not subject to devastating floods.


title: Ghaggar-Hakra River

text: Khonde et al. (2017) confirm that the Great Rann of Kutch received sediments from a different source than the Indus, but this source stopped supplying sediments after ca. 10,000 years ago. Likewise, Dave et al. (2019) state that "[o]ur results disprove the proposed link between ancient settlements and large rivers from the Himalayas and indicate that the major palaeo-fluvial system traversing through this region ceased long before the establishment of the Harappan civilisation."


title: Ghaggar-Hakra River

text: During the IVC, the Ghaggar-Hakra fluvial system was not a large glacier-fed Himalayan river, but a monsoonal-fed river. The Indus Valley Civilisation prospered when the monsoons that fed the rivers diminished around 5,000 years ago, and a large number of sites from the Mature Indus Valley civilisation (2600-1900 BCE) are found along the middle course of the (dried-up) Hakra in Pakistan. Around 4,000 the Indus Valley Civilisation declined when the monsoons further diminished, and the Ghaggar-Hakra dried-up, becoming a small seasonal river.


title: Ghaggar-Hakra River

text: According to archaeologist Rita Wright, the large number of documented sites may be due to the ephemeral nature of the settlements, with the inhabitants frequently moving around in pursuit of water. According to archaeologist Shereen Ratnagar, many Ghaggar-Hakra sites in India are actually those of local cultures; some sites display contact with Harappan civilisation, but only a few are fully developed Harappan ones. Hetalben Sidhav notes that claims of a large number of Ghaggar-Hakra sites are politically motivated and exaggerated. While the Indus remained an active river, the Ghaggar-Hakra dried up, leaving many sites undisturbed, which explains why such a large number of sites has been found.


title: Ghaggar-Hakra River

text: Late in the 2nd millennium BCE the Ghaggar-Hakra fluvial system dried up, becoming the small seasonal river it is today, which affected the Harappan civilisation. Paleobotanical information documents the aridity that developed after the drying up of the river. The diminishing of the monsoons particular effected the Ghaggar-Hakra system, which became ephemeral and was largely abandoned, with the IVC reorganizing in local settlements some 4000 years ago. In the late Harappan period the number of late Harappan sites in the middle Ghaggar-Hakra channel and in the Indus valley diminished, while it expanded in the upper Ghaggar-Sutlej channels and in Saurashtra. The IVC-people migrated east toward the more humid regions of the Indo-Gangetic Plain, where the decentralised late Harappan phase took place.


title: Ghaggar-Hakra River

text: The same widespread aridification in the third millennium BCE also led to water shortages and ecological changes in the Eurasian steppes, leading to a change of vegetation, triggering "higher mobility and transition to nomadic cattle breeding," These migrations eventually resulted in the Indo-Aryan migrations into South Asia.


title: Ghaggar-Hakra River

text: Most of the Harappan sites along the Ghaggar-Hakra are presently found in desert country, and have remained undisturbed since the end of the Indus Civilization. This contrasts with the heavy alluvium of the Indus and other large Panjab rivers that have obscured Harappan sites, including part of Mohenjo Daro. Painted Grey Ware sites ( 1000–600 BCE) have been found at former IVC-sites at the middle and upper Ghaggar-Hakra channel, and have also been found in the bed and not on the banks of the Ghaggar-Hakra river, which suggests that river was certainly dried up by this period. The sparse distribution of the Painted Gray Ware sites in the Ghaggar river valley indicates that during this period the Ghaggar river had already dried up.


title: Ghaggar-Hakra River

text: Since the 19th century, proposals have been made to identify the mythological Sarasvati River with the Ghaggar-Hakra River. The Sarasvati is often mentioned in the Rig Veda, which describes it as a mighty river located between the Indus and the Ganges, while later Vedic texts describe it as disappearing in the desert. Arguments have been made that the Ghaggar-Hakra was such a mighty river, due to tributaries which were supposed to receive snow melt waters from the Himalayas. Yet, more recent research shows that the Ghaggar-Hakra was monsoon-fed during Harappan times, and had already dried-up during Vedic times.


title: Ghaggar-Hakra River

text: The Sarasvati River is mentioned in all books of the Rigveda except the fourth. It is the only river with hymns entirely dedicated to it: RV 6.61, RV 7.95 and RV 7.96. It is mentioned as a divine and large river, which flows "from the mountains to the samudra," which some take as the Indian Ocean. The Rig Veda was composed during the latter part of the late Harappan period, and according to Shaffer, the reason for the predominance of the Sarasvati in the Rig Veda is the late Harappan (1900–1300 BCE) population shift eastwards to Haryana.


title: Ghaggar-Hakra River

text: The identification with the Sarasvati River is based on the mentions in Vedic texts, "e.g." in the enumeration of the rivers in Rigveda 10.75.05; the order is Ganga, Yamuna, Sarasvati, Sutudri, Parusni. Later Vedic texts record the river as disappearing at Vinasana (literally, "the disappearing") or Upamajjana, and in post-Vedic texts as joining both the Yamuna and Ganges as an invisible river at Prayaga (Allahabad). Some claim that the sanctity of the modern Ganges is directly related to its assumption of the holy, life-giving waters of the ancient Saraswati River. The Mahabharata says that the Sarasvati River dried up in a desert (at a place named Vinasana or Adarsana).


title: Ghaggar-Hakra River

text: Nineteenth and early 20th century scholars, such as orientalist Christian Lassen (1800–1876), philologist and Indologist Max Müller (1823–1900), archaeologist Aurel Stein (1862–1943), and geologist R. D. Oldham (1858–1936), had considered that the Ghaggar-Hakra might be the defunct remains of a river, the Sarasvati, invoked in the orally transmitted collection of ancient Sanskrit hymns, the Rig Veda composed circa 1500 BCE to 1200 BCE.


title: Ghaggar-Hakra River

text: More recently, but writing before Giosan's 2012 publication and supposing a late Harappan diversion of the Sutlej and the Yamuna, several scholars have identified the old Ghaggar-Hakra River with the Vedic Sarasvati River and the Chautang with the Drishadvati River. Gregory Possehl and Jane McIntosh refer to the Ghaggar-Hakra River as "Sarasvati" throughout their respective 2002 and 2008 books on the Indus Civilisation, and Gregory Possehl states "Linguistic, archaeological, and historical data show that the Sarasvati of the Vedas is the modern Ghaggar or Hakra."


title: Ghaggar-Hakra River

text: Because most of the Indus Valley sites known so far are actually located on the Ghaggar-Hakra river and its tributaries and not on the Indus river, some Indian archaeologists, such as S.P. Gupta, have proposed to use the term "Indus Sarasvati Civilization" to refer to the Harappan culture which is named, as is common in archaeology, after the first place where the culture was discovered.


title: Ghaggar-Hakra River

text: Romila Thapar terms the identification "controversial" and dismisses it, noticing that the descriptions of Sarasvati flowing through the "high mountains" does not tally with Ghaggar's course and suggests that Sarasvati is Haraxvati of Afghanistan which is also known as the Helmand river. Wilke suggests that the identification is problematic since the Ghaggar-Hakra river was already dried up at the time of the composition of the Vedas, let alone the migration of the Vedic people into northern India.


title: Ghaggar-Hakra River

text: The idea that the Ghaggar-Hakra was fed by Himalayan sources has also been contradicted by recent geophysical research, which shows that the Ghaggar-Hakra system, although having greater discharge in Harappan times which was enough to sustain human habitation, was not sourced by the glaciers and snows of the Himalayas, but rather by a system of perennial monsoon-fed rivers. In contrast to all Himalayan rivers in the region that dug out wide valleys in their own sediments as the monsoon declined, no such valley exists between the Sutlej and the Yamuna, demonstrating that neither the Ghaggar-Hakra nor any other Sarasvati candidate in that region had a Himalayan source.


title: Ghaggar-Hakra River

text: Rajesh Kocchar further notes that, even if the Sutlej and the Yamuna had drained into the Ghaggar during Vedic period, it still would not fit the Rig Vedic descriptions because "the snow-fed Satluj and Yamuna would strengthen [only the] lower Ghaggar. [The] upper Ghaggar would still be as puny as it is today." According to Rajesh Koccha there are two Sarasvati rivers mentioned in the Rigveda. The older one described in the family books of the Rigveda, which he calls "Naditama Sarasvati", drains into a samudra. The newer one described in the tenth book of Rigveda as well as later Vedic texts, which he calls "Vinasana Sarasvati", disappears in the sands. The "Vinasana Sarasvati" has been "accepted by all" to be the same as the Ghaggar-Hakra river. The description of the "Naditama Sarasvati" in the Rigveda matches the physical features of the Helmand River in Afghanistan, more precisely its tributary the Harut River, whose older name was "Haraxatī" in Avestan. Ganga and Yamuna, he takes to be small streams in its vicinity. When the Vedic people moved east into Punjab, they named the new rivers they encountered after the old rivers they knew from Helmand.


title: Republic of Biak-na-Bato

text: Republic of Biak-na-Bato is a designation referring to the second revolutionary republican government led by Emilio Aguinaldo during the Philippine Revolution, That government referred to itself as Republic of the Philippines (; in modern ) and was seated in what is now Biak-na-Bato National Park. The current designation was adopted by historians to avoid confusion with name of the current Philippine government, which also refers to itself the "Republic of the Philippines", and with other past Philippine governments using the same designation.


title: Republic of Biak-na-Bato

text: The Biak-na-Bato republic lasted just over a month. It was disestablished by a peace treaty signed by Aguinaldo and the Spanish Governor-General, Fernando Primo de Rivera, which included provision for exile of Aguinaldo and key associates to Hong Kong.


title: Republic of Biak-na-Bato

text: The Republic of Biak-na-Bato was one of a number of Filipino revolutionary states that were formed to expel the Spanish colonial regime in the Philippines and were not able to receive international recognition. It was preceded and succeeded by two similarly unrecognized states, the Tejeros government and the Central Executive Committee.


title: Republic of Biak-na-Bato

text: The constitution of the Republic of Biak-na-Bato was written by Felix Ferrer and Isabelo Artacho, who copied the Cuban Constitution of Jimaguayú nearly word-for-word. It provided for the creation of a Supreme Council, which was created on November 1, 1897, with the following as officers having been elected:


title: Republic of Biak-na-Bato

text: The initial concept of the republic began during the latter part of the Philippine Revolution, when the now-undisputed leader of the Revolution, Emilio Aguinaldo, became surrounded by Spanish forces at his headquarters in Talisay, Batangas. Aguinaldo slipped through the Spanish cordon and, with 500 picked men, proceeded to Biak-na-Bató, ("Cleft Rock"; in modern ) a wilderness area at the town of San Miguel, Bulacan (now parts of San Miguel, San Ildefonso and Doña Remedios in Bulacan). When news of Aguinaldo's arrival there reached the towns of central Luzon, men from the Ilocos provinces, Nueva Ecija, Pangasinan, Tarlac, and Zambales renewed their armed resistance against the Spanish.


title: Republic of Biak-na-Bato

text: Unable to persuade the revolutionaries to give up their arms, Governor-General Primo de Rivera issued a decree on July 2, 1897, which prohibited inhabitants from leaving their villages and towns. Contrary to his expectations, they continued fighting. Within days, Aguinaldo and his men planned the establishment of a Republic. Aguinaldo issued a proclamation from his hideout in Biak-na-Bato entitled "To the Brave Sons of the Philippines", in which he listed his revolutionary demands as:


title: Republic of Biak-na-Bato

text: By the end of 1897, Governor-General Primo de Rivera accepted the impossibility of quelling the revolution by force of arms. In a statement to the "Cortes Generales", he said, ""I can take Biak-na-Bato, any military man can take it, but I can not answer that I could crush the rebellion."" Desiring to make peace with Aguinaldo, he sent emissaries to Aguinaldo seeking a peaceful settlement. Ironically, nothing was accomplished until Pedro A. Paterno, a known turncoat and a lawyer from Manila, volunteered to act as negotiator.


title: Republic of Biak-na-Bato

text: On August 9, 1897, Paterno proposed a peace based on reforms and amnesty to Aguinaldo. In succeeding months, practicing shuttle diplomacy, Paterno traveled back and forth between Manila and Biak-na-Bato carrying proposals and counterproposals. Paterno's efforts led to a peace agreement called the Pact of Biak-na-Bato. This consisted of three documents, the first two being signed on December 14, 1897, and the third being signed on December 15; effectively ending the Republic of Biak-na-Bato.


title: Republic of Biak-na-Bato

text: On November 16, 1937, a 2,117-hectare block in the Biak-na-Bato area was declared a national park by Manuel L. Quezon in honor of the Republic. In the 1970s, Ferdinand Marcos issued orders guiding mineral prospecting and exploitation in government reservation, impacting the park's boundaries. On April 11, 1989, Corazon Aquino issued Proclamation No. 401, which re-defined the boundaries of the Biak-na-Bato National Park. The proclamation set aside hectares as mineral reservation, hectares as watershed reservation and hectares as forest reserve.


title: Shashikala

text: Shashikala Saigal (née Jawalkar; 4 August 1932 – 4 April 2021), better known by her first name, was an Indian film and television actress, who played supporting roles in hundreds of Bollywood films beginning in the 1940s.


title: Shashikala

text: Shashikala Jawalkar was one of six children born in Solapur, Maharashtra to a Hindu Bhavsar Shimpi caste Marathi speaking family. By age 5, she had already been dancing, singing and acting on stage in many towns in Solapur district. When Shashikala was in her pre-teens, through ill luck, her father became bankrupt, and he brought his family to Bombay (now Mumbai), where they thought that Shashikala, the best-looking and most-talented among his children, could find work in movies. For some time, the family lived with friends and barely survived, while Shashikala wandered from one studio to another looking for work. She earned in bits and pieces till she met Noor Jehan, the reigning screen queen.


title: Shashikala

text: Noor Jehan's husband Shaukat Hussain Rizvi, was making the movie "Zeenat" then, and included Shashikala in a "Qawwali" scene. She worked with Shammi Kapoor in film Daku (1955). She struggled on and got small roles in movies made by P. N. Arora, Amiya Chakravarti, and a few other producers. She first rose to fame with her role in Hindi film Pugdi (1948) produced by Prem Narayan Arora. She got roles in V. Shantaram's "Teen Batti Char Raasta" (1953) and a few other movies. While in her early twenties, Shashikala met and married Om Prakash Saigal, who belonged to the Kundan Lal Saigal family, and has two daughters.


title: Shashikala

text: In 1959, she appeared in Bimal Roy's "Sujata". In Tarachand Barjatya's "Aarti" (1962), starring Meena Kumari, Ashok Kumar, and Pradeep Kumar, Shashikala portrayed a negative role, eventually winning a Filmfare Award. Soon after, offers began to pour in to her for supporting roles. She appeared in "Anupama", "Phool Aur Patthar", "Ayi Milan Ki Bela", "Gumrah", "Waqt", and "Khubsoorat". She played a negative character in Chhote Sarkar (1974) starring Shammi Kapoor and Sadhana. While her female lead co-stars usually played roles of good-natured, modest, or pious women, Shashikala usually played either flighty and feisty bubbly women or vamps who plotted the downfall of others. Later in her acting career, she would typically play the role of a sister or mother-in-law. In 80s her acclaimed performances came in films like Phir Wahi Raat, Souten, Sargam. She performed in supporting roles in more than 100 films.


title: Shashikala

text: In the past years, she has performed in a few television serials, including "Jeena Isi Ka Naam Hai" for Sony, "Apnaapan" for Zee TV, "Dil Deke Dekho" for Sab TV and "Son Pari" for Star Plus. She had roles in "Mother 98", "Pardesi Babu", "Baadshah", "Kabhi Khushi Kabhie Gham", "Mujhse Shaadi Karogi" and "Chori Chori".


title: Radon–Nikodym theorem

text: In mathematics, the Radon–Nikodym theorem is a result in measure theory that expresses the relationship between two measures defined on the same measurable space. A "measure" is a set function that assigns a consistent magnitude to the measurable subsets of a measurable space. Examples of a measure include area and volume, where the subsets are sets of points; or the probability of an event, which is a subset of possible outcomes within a wider probability space.


title: Radon–Nikodym theorem

text: One way to derive a new measure from one already given is to assign a density to each point of the space, then integrate over the measurable subset of interest. This can be expressed as


title: Radon–Nikodym theorem

text: where is the new measure being defined for any measurable subset and the function is the density at a given point. The integral is with respect to an existing measure , which may often be the canonical Lebesgue measure on the real line or the "n"-dimensional Euclidean space (corresponding to our standard notions of length, area and volume). For example, if represented mass density and was the Lebesgue measure in three-dimensional space , then would equal the total mass in a spatial region .


title: Radon–Nikodym theorem

text: The Radon–Nikodym theorem essentially states that, under certain conditions, any measure can be expressed in this way with respect to another measure on the same space. The function is then called the Radon–Nikodym derivative and is denoted by formula_2. An important application is in probability theory, leading to the probability density function of a random variable.


title: Radon–Nikodym theorem

text: The theorem is named after Johann Radon, who proved the theorem for the special case where the underlying space is in 1913, and for Otto Nikodym who proved the general case in 1930. In 1936 Hans Freudenthal generalized the Radon–Nikodym theorem by proving the Freudenthal spectral theorem, a result in Riesz space theory; this contains the Radon–Nikodym theorem as a special case.


title: Radon–Nikodym theorem

text: A Banach space is said to have the Radon–Nikodym property if the generalization of the Radon–Nikodym theorem also holds, "mutatis mutandis", for functions with values in . All Hilbert spaces have the Radon–Nikodym property.


title: Radon–Nikodym theorem

text: The Radon–Nikodym theorem involves a measurable space formula_3 on which two σ-finite measures are defined, formula_4 and formula_5


title: Radon–Nikodym theorem

text: It states that, if formula_6 (that is, if formula_7 is absolutely continuous with respect to formula_4), then there exists a formula_9-measurable function formula_10 such that for any measurable set formula_11


title: Radon–Nikodym theorem

text: The function formula_13 satisfying the above equality is , that is, if formula_14 is another function which satisfies the same property, then formula_15 . The function formula_13 is commonly written formula_17 and is called the . The choice of notation and the name of the function reflects the fact that the function is analogous to a derivative in calculus in the sense that it describes the rate of change of density of one measure with respect to another (the way the Jacobian determinant is used in multivariable integration).


title: Radon–Nikodym theorem

text: A similar theorem can be proven for signed and complex measures: namely, that if formula_4 is a nonnegative σ-finite measure, and formula_7 is a finite-valued signed or complex measure such that formula_20 that is, formula_7 is absolutely continuous with respect to formula_22 then there is a formula_4-integrable real- or complex-valued function formula_14 on formula_25 such that for every measurable set formula_26


title: Radon–Nikodym theorem

text: In the following examples, the set is the real interval [0,1], and formula_9 is the Borel sigma-algebra on .


title: Radon–Nikodym theorem

text: The theorem is very important in extending the ideas of probability theory from probability masses and probability densities defined over real numbers to probability measures defined over arbitrary sets. It tells if and how it is possible to change from one probability measure to another. Specifically, the probability density function of a random variable is the Radon–Nikodym derivative of the induced measure with respect to some base measure (usually the Lebesgue measure for continuous random variables).


title: Radon–Nikodym theorem

text: For example, it can be used to prove the existence of conditional expectation for probability measures. The latter itself is a key concept in probability theory, as conditional probability is just a special case of it.


title: Radon–Nikodym theorem

text: Amongst other fields, financial mathematics uses the theorem extensively, in particular via the Girsanov theorem. Such changes of probability measure are the cornerstone of the rational pricing of derivatives and are used for converting actual probabilities into those of the risk neutral probabilities.


title: Radon–Nikodym theorem

text: The Radon–Nikodym theorem above makes the assumption that the measure "μ" with respect to which one computes the rate of change of "ν" is σ-finite.


title: Radon–Nikodym theorem

text: Consider the Borel σ-algebra on the real line. Let the counting measure, , of a Borel set be defined as the number of elements of if is finite, and otherwise. One can check that is indeed a measure. It is not -finite, as not every Borel set is at most a countable union of finite sets. Let be the usual Lebesgue measure on this Borel algebra. Then, is absolutely continuous with respect to , since for a set one has only if is the empty set, and then is also zero.


title: Radon–Nikodym theorem

text: for all real numbers . This implies that the function , and therefore the Lebesgue measure , is zero, which is a contradiction.


title: Radon–Nikodym theorem

text: Assuming formula_58 the Radon–Nikodym theorem also holds if formula_4 is localizable and formula_7 is "accessible with respect to" formula_4, i.e., formula_62 for all formula_63


title: Radon–Nikodym theorem

text: This section gives a measure-theoretic proof of the theorem. There is also a functional-analytic proof, using Hilbert space methods, that was first given by von Neumann.


title: Radon–Nikodym theorem

text: For finite measures and , the idea is to consider functions with . The supremum of all such functions, along with the monotone convergence theorem, then furnishes the Radon–Nikodym derivative. The fact that the remaining part of is singular with respect to follows from a technical fact about finite measures. Once the result is established for finite measures, extending to -finite, signed, and complex measures can be done naturally. The details are given below.


title: Radon–Nikodym theorem

text: Constructing an extended-valued candidate First, suppose and are both finite-valued nonnegative measures. Let be the set of those extended-value measurable functions such that:


title: Radon–Nikodym theorem

text: , since it contains at least the zero function. Now let , and suppose is an arbitrary measurable set, and define:


title: Radon–Nikodym theorem

text: By replacing with the maximum of the first functions, one can assume that the sequence is increasing. Let be an extended-valued function defined as


title: Radon–Nikodym theorem

text: Suppose ; then, since is finite, there is an such that . To derive a contradiction from , we look for a positive set for the signed measure (i.e. a measurable set , all of whose measurable subsets have non-negative measure), where also has positive -measure. Conceptually, we're looking for a set , where in every part of . A convenient approach is to use the Hahn decomposition for the signed measure .


title: Radon–Nikodym theorem

text: where is the indicator function of . Also, note that as desired; for if , then (since is absolutely continuous in relation to ) , so and


title: Radon–Nikodym theorem

text: This is impossible because it violates the definition of a supremum; therefore, the initial assumption that must be false. Hence, , as desired.


title: Radon–Nikodym theorem

text: Restricting to finite values Now, since is -integrable, the set is -null. Therefore, if a is defined as


title: Radon–Nikodym theorem

text: If and are -finite, then can be written as the union of a sequence of disjoint sets in , each of which has finite measure under both and . For each , by the finite case, there is a -measurable function such that


title: Radon–Nikodym theorem

text: for each -measurable subset of . The sum formula_81 of those functions is then the required function such that formula_82.


title: Radon–Nikodym theorem

text: If is a -finite signed measure, then it can be Hahn–Jordan decomposed as where one of the measures is finite. Applying the previous result to those two measures, one obtains two functions, , satisfying the Radon–Nikodym theorem for and respectively, at least one of which is -integrable (i.e., its integral with respect to is finite). It is clear then that satisfies the required properties, including uniqueness, since both and are unique up to -almost everywhere equality.


title: Radon–Nikodym theorem

text: If is a complex measure, it can be decomposed as , where both and are finite-valued signed measures. Applying the above argument, one obtains two functions, , satisfying the required properties for and , respectively. Clearly, is the required function.


title: Radon–Nikodym theorem

text: Lebesgue's decomposition theorem shows that the assumptions of the Radon–Nikodym theorem can be found even in a situation which is seemingly more general. Consider a σ-finite positive measure formula_4 on the measure space formula_84 and a σ-finite signed measure formula_7 on formula_9, without assuming any absolute continuity. Then there exist unique signed measures formula_87 and formula_88 on formula_9 such that formula_90, formula_91, and formula_92. The Radon–Nikodym theorem can then be applied to the pair formula_93.


title: Electromagnetic absorption by water

text: The absorption in the gas phase occurs in three regions of the spectrum. Rotational transitions are responsible for absorption in the microwave and far-infrared, vibrational transitions in the mid-infrared and near-infrared. Vibrational bands have rotational fine structure. Electronic transitions occur in the vacuum ultraviolet regions.


title: Electromagnetic absorption by water

text: Liquid water has no rotational spectrum but does absorb in the microwave region. Its weak absorption in the visible spectrum results in the pale blue color of water.


title: Electromagnetic absorption by water

text: The water molecule, in the gaseous state, has three types of transition that can give rise to absorption of electromagnetic radiation:


title: Electromagnetic absorption by water

text: In reality, vibrations of molecules in the gaseous state are accompanied by rotational transitions, giving rise to a vibration-rotation spectrum. Furthermore, vibrational overtones and combination bands occur in the near-infrared region. The HITRAN spectroscopy database lists more than 37,000 spectral lines for gaseous HO, ranging from the microwave region to the visible spectrum.


title: Electromagnetic absorption by water

text: In liquid water the rotational transitions are effectively quenched, but absorption bands are affected by hydrogen bonding. In crystalline ice the vibrational spectrum is also affected by hydrogen bonding and there are lattice vibrations causing absorption in the far-infrared. Electronic transitions of gaseous molecules will show both vibrational and rotational fine structure.


title: Electromagnetic absorption by water

text: Infrared absorption band positions may be given either in wavelength (usually in micrometers, μm) or wavenumber (usually in reciprocal centimeters, cm) scale.


title: Electromagnetic absorption by water

text: The water molecule is an asymmetric top, that is, it has three independent moments of inertia. Rotation about the 2-fold symmetry axis is illustrated at the left. Because of the low symmetry of the molecule, a large number of transitions can be observed in the far infrared region of the spectrum. Measurements of microwave spectra have provided a very precise value for the O−H bond length, 95.84 ± 0.05 pm and H−O−H bond angle, 104.5 ± 0.3°.


title: Electromagnetic absorption by water

text: The water molecule has three fundamental molecular vibrations. The O-H stretching vibrations give rise to absorption bands with band origins at 3657 cm (ν, 2.734 μm) and 3756 cm (ν, 2.662 μm) in the gas phase. The asymmetric stretching vibration, of B symmetry in the point group C is a normal vibration. The H-O-H bending mode origin is at 1595 cm (ν, 6.269 μm). Both symmetric stretching and bending vibrations have A symmetry, but the frequency difference between them is so large that mixing is effectively zero. In the gas phase all three bands show extensive rotational fine structure. In the Near-infrared spectrum


title: Electromagnetic absorption by water

text: ν has a series of overtones at wavenumbers somewhat less than n·ν, n=2,3,4,5... Combination bands, such as ν + ν are also easily observed in the near-infrared region. The presence of water vapor in the atmosphere is important for atmospheric chemistry especially as the infrared and near infrared spectra are easy to observe. Standard (atmospheric optical) codes are assigned to absorption bands as follows. 0.718 μm (visible): α, 0.810 μm: μ, 0.935 μm: ρστ, 1.13 μm: φ, 1.38 μm: ψ, 1.88 μm: Ω, 2.68 μm: X. The gaps between the bands define the infrared window in the Earth's atmosphere.


title: Electromagnetic absorption by water

text: The infrared spectrum of liquid water is dominated by the intense absorption due to the fundamental O-H stretching vibrations. Because of the high intensity, very short path lengths, usually less than 50 μm, are needed to record the spectra of aqueous solutions. There is no rotational fine structure, but the absorption bands are broader than might be expected, because of hydrogen bonding. Peak maxima for liquid water are observed at 3450 cm (2.898 μm), 3615 cm (2.766 μm) and 1640 cm (6.097 μm). Direct measurement of the infrared spectra of aqueous solutions requires that the cuvette windows be made of substances such as calcium fluoride which are water-insoluble. This difficulty can alternatively be overcome by using an attenuated total reflectance (ATR) device rather than transmission.


title: Electromagnetic absorption by water

text: In the near-infrared range liquid water has absorption bands around 1950 nm (5128 cm), 1450 nm (6896 cm), 1200 nm (8333 cm) and 970 nm, (10300 cm). The regions between these bands can be used in near-infrared spectroscopy to measure the spectra of aqueous solutions, with the advantage that glass is transparent in this region, so glass cuvettes can be used. The absorption intensity is weaker than for the fundamental vibrations, but this is not important as longer path-length cuvettes can be used. The absorption band at 698 nm (14300 cm) is a 3rd overtone (n=4). It tails off onto the visible region and is responsible for the intrinsic blue color of water. This can be observed with a standard UV/vis spectrophotometer, using a 10 cm path-length. The colour can be seen by eye by looking through a column of water about 10 m in length; the water must be passed through an ultrafilter to eliminate color due to Rayleigh scattering which also can make water appear blue.


title: Electromagnetic absorption by water

text: The spectrum of ice is similar to that of liquid water, with peak maxima at 3400 cm (2.941 μm), 3220 cm (3.105 μm) and 1620 cm (6.17 μm)


title: Electromagnetic absorption by water

text: In both liquid water and ice clusters, low-frequency vibrations occur, which involve the stretching (TS) or bending (TB) of intermolecular hydrogen bonds (O–H•••O). Bands at wavelengths λ = 50-55 μm or 182-200 cm (44 μm, 227 cm in ice) have been attributed to TS, intermolecular stretch, and 200 μm or 50 cm (166 μm, 60 cm in ice), to TB, intermolecular bend


title: Electromagnetic absorption by water

text: Absorption coefficients for 200 nm and 900 nm are almost equal at 6.9 m (attenuation length of 14.5 cm). Very weak light absorption, in the visible region, by liquid water has been measured using an integrating cavity absorption meter (ICAM). The absorption was attributed to a sequence of overtone and combination bands whose intensity decreases at each step, giving rise to an absolute minimum at 418 nm, at which wavelength the attenuation coefficient is about 0.0044 m, which is an attenuation length of about 227 meters. These values correspond to pure absorption without scattering effects. The attenuation of, e.g., a laser beam would be slightly stronger.


title: Electromagnetic absorption by water

text: The electronic transitions of the water molecule lie in the vacuum ultraviolet region. For water vapor the bands have been assigned as follows.


title: Electromagnetic absorption by water

text: Liquid water has a broad absorption spectrum in the microwave region, which has been explained in terms of changes in the hydrogen bond network giving rise to a broad, featureless, microwave spectrum. The absorption (equivalent to dielectric loss) is used in microwave ovens to heat food that contains water molecules. A frequency of 2.45 GHz, wavelength 122 mm, is commonly used.


title: Electromagnetic absorption by water

text: Radiocommunication at GHz frequencies is very difficult in fresh waters and even more so in salt waters.


title: Electromagnetic absorption by water

text: Water vapor is a greenhouse gas in the Earth's atmosphere, responsible for 70% of the known absorption of incoming sunlight, particularly in the infrared region, and about 60% of the atmospheric absorption of thermal radiation by the Earth known as the greenhouse effect. It is also an important factor in multispectral imaging and hyperspectral imaging used in remote sensing because water vapor absorbs radiation differently in different spectral bands. Its effects are also an important consideration in infrared astronomy and radio astronomy in the microwave or millimeter wave bands. The South Pole Telescope was constructed in Antarctica in part because the elevation and low temperatures there mean there is very little water vapor in the atmosphere.


title: Electromagnetic absorption by water

text: Similarly, carbon dioxide absorption bands occur around 1400, 1600 and 2000 nm, but its presence in the Earth's atmosphere accounts for just 26% of the greenhouse effect. Carbon dioxide gas absorbs energy in some small segments of the thermal infrared spectrum that water vapor misses. This extra absorption within the atmosphere causes the air to warm just a bit more and the warmer the atmosphere the greater its capacity to hold more water vapor. This extra water vapor absorption further enhances the Earth's greenhouse effect.