hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Support (measure theory)
In mathematics, the support (sometimes topological support or spectrum) of a measure  on a measurable topological space  is a precise notion of where in the space  the measure "lives". It is defined to be the largest (closed) subset of  for which every open neighbourhood of every point of the set has positive measure.

Subset
In mathematics, a set A is a subset of a set B if and only if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements.

When quantified,  is represented as

One can prove the statement  by applying a proof technique known as the element argument:

Let sets A and B be given. To prove that 
suppose that a is a particular but arbitrarily chosen element of A
show that a is an element of B.

The validity of this technique can be seen as a consequence of universal generalization: the technique shows  for an arbitrarily chosen element c. Universal generalisation then implies  which is equivalent to  as stated above.
The Voice of Poland season 15
The fifteenth season of the Polish singing competition The Voice of Poland began airing on September 7, 2024, on TVP 2. It is airing on Saturdays at 20:00. Tomson & Baron and Lanberry returned to the show as coaches for their thirteenth and third seasons, respectively. Additionally, Michał Szpak returned to the show after his three-year hiatus for his fifth season, alongside Kuba Badach, who made his debut as a coach this season.

Anna Iwanek won the season, marking Kuba Badach's first win as a coach. With Iwanek's win, Badach became the fourth coach, after Marek Piekarczyk,  Maria Sadowska and Michał Szpak to win on their debut season. In addition, this also marks the first winning artist that had a coach (2 in this instance) blocked in their blind audition (Lanberry blocking Michał, then Tomson & Baron blocking Lanberry).

TVP2
TVP2 (TVP Dwa, Telewizja Polska 2, Program Drugi Telewizji Polskiej, "Dwójka") is a Polish public mainstream TV channel operated by TVP. Launched in October 1970, its varied line-up contains a variety of programming (documentary, history, talk-shows, game-shows) although it focuses on entertainment: stand up comedy, comic shows, cabaret, and themed talk shows (for example on travel or foreign cultures).

TVP2 is broadcast as part of the nationwide, unencrypted (free-to-air) third multiplex of digital terrestrial television (MUX 3). It is also available on all cable networks and satellite digital platforms in accordance with the so-called must-carry rule—a provision in the Broadcasting and Television Act requiring every television operator to offer seven specific channels: TVP1, TVP2, and TVP3, as well as four commercial ones – TVN, Polsat, TV4, and TV Puls.

TVP2 can also be watched for free online through services such as TVP VOD and TVP GO.
Druzhnaya Gorka
Druzhnaya Gorka (Russian: Дружная Горка) is the name of several inhabited localities in Russia.

Urban localities

Druzhnaya Gorka, Leningrad Oblast, an urban-type settlement under the administrative jurisdiction of Druzhnogorskoye Settlement Municipal Formation in Gatchinsky District of Leningrad Oblast; 59°17′N 30°8′E﻿ / ﻿59.283°N 30.133°E﻿ / 59.283; 30.133

Rural localities

Druzhnaya Gorka, Novgorod Oblast, a village in Berezovikskoye Settlement of Okulovsky District in Novgorod Oblast

Druzhnaya Gorka, Tver Oblast, a village in Okovetskoye Rural Settlement of Selizharovsky District in Tver Oblast

Selizharovsky District
Selizharovsky District  (Russian: Селижа́ровский райо́н) is an administrative and municipal district (raion), one of the thirty-six in Tver Oblast, Russia. It is located in the western central part of the oblast and borders with Ostashkovsky District in the north, Kuvshinovsky District in the northeast, Staritsky District in the east, Rzhevsky District in the southeast, Oleninsky District in the south, Nelidovsky District in the southwest, Andreapolsky District in the west, and with Penovsky District in the northwest. The area of the district is 3,098 square kilometers (1,196 sq mi). Its administrative center is the urban locality (an urban-type settlement) of Selizharovo. Population: 12,722 (2010 Census);  15,125 (2002 census); 18,092 (1989 Soviet census). The population of Selizharovo accounts for 52.9% of the district's total population.
Dabataw
Dabataw is a village in Ye Township in Mawlamyine District in the Mon State of south-east Burma (Myanmar). Dabataw is on a tributary of the Palantha Chaung, in the foothills of the Tenasserim Range, about 2 kilometres (1.2 mi) east of Waipathe.

Mawlamyine District
Mawlamyine District (Burmese: မော်လမြိုင်ခရိုင်) is a(Mon language :ခရီုမတ်မလီု) district of the Mon State in Myanmar (Burma). The capital is Mawlamyine town. The district covers an area of 6,084 km2, and had a population of 1,232,221 at the 2014 Census.
Javianne Oliver
Javianne Oliver (born December 26, 1994) is an American female track and field sprinter.

Oliver finished second in the 60 meters at the 2017 NCAA Division I Indoor Track and Field Championships for the University of Kentucky.

Oliver won the 60 meters at the 2018 USA Indoor Track and Field Championships to qualify for the 2018 IAAF World Indoor Championships.  Her time of 7.02 was the top time that season in the world.  She returned to the 2020 USA Track & Field Indoor Championships to finish second to Mikiah Brisco, qualifying to her second World Championships in the process. Oliver also won the 2020 US Olympic Trials with a time of 10.99.

2017 NCAA Division I Indoor Track and Field Championships
The 2017 NCAA Division I Indoor Track and Field Championships was the 53rd NCAA Men's Division I Indoor Track and Field Championships and the 36th NCAA Women's Division I Indoor Track and Field Championships, held at the Gilliam Indoor Track Stadium in College Station, Texas near the campus of the host school, the Texas A&M University. In total, thirty-four different men's and women's indoor track and field events were contested from March 10 to March 11, 2017.
Titus and Berenice
Titus and Berenice is a 1676 tragedy by the English writer Thomas Otway. It portrays the relationship between the Roman Emperor Titus and the Jewish Queen Berenice. It premiered at the Dorset Garden Theatre, staged by the Duke's Company. It was inspired by Jean Racine's 1670 French work Bérénice.

The original cast included Thomas Betterton as Titus Vespatian, William Smith as Antiochus, Matthew Medbourne as Paulinus, John Crosby as Arsaces, Thomas Gillow as Rutilius, Mary Lee as Berenice and Elizabeth Barry as Phaenice. Another new work by Otway, a farce The Cheats of Scapin was performed as an afterpiece. Both plays were published together the following year and dedicated to the Earl of Rochester.

Dorset Garden Theatre
51°30′51″N 0°6′29″W﻿ / ﻿51.51417°N 0.10806°W﻿ / 51.51417; -0.10806

The Dorset Garden Theatre in London, built in 1671, was in its early years also known as the Duke of York's Theatre, or the Duke's Theatre. In 1685, King Charles II died and his brother, the Duke of York, was crowned as James II. When the Duke became King, the theatre became the Queen's Theatre in 1685, referring to James' second wife, Mary of Modena. The name remained when William III and Mary II came to the throne in 1689.

It was the fourth home of the Duke's Company, one of the two patent theatre companies in Restoration London, and after 1682 continued to be used by the company's successor, the United Company.

It was demolished in 1709.
Elachista
Elachista is a genus of gelechioid moths described by Georg Friedrich Treitschke in 1833. It is the type genus of the grass-miner moth family (Elachistidae). This family is sometimes (in particular in older sources) circumscribed very loosely, including for example the Agonoxenidae and Ethmiidae which seem to be quite distinct among the Gelechioidea, as well as other lineages which are widely held to be closer to Oecophora than to Elachista and are thus placed in the concealer moth family Oecophoridae here.

These grass-miners are very small moths with the "feathery" hindwings characteristic of their family. They are essentially found worldwide, except in very cold places and on some oceanic islands; as usual for Gelechioidea, they are most common in the Palearctic however. They usually have at least one, sometimes as many as three light bands running from leading to trailing edge of their forewing uppersides. Some species, however, have upper forewings that are mostly white.

Oecophoridae
Oecophoridae (concealer moths) is a family of small moths in the superfamily Gelechioidea. The phylogeny and systematics of gelechoid moths are still not fully resolved, and the circumscription of the Oecophoridae is strongly affected by this.
Committee on Small Business
Committee on Small Business or Small Business Committee can refer to:

United States House Committee on Small Business
United States House Small Business Subcommittee on Health and Technology
United States House Small Business Subcommittee on Agriculture, Energy and Trade
United States House Small Business Subcommittee on Contracting and Workforce
United States House Small Business Subcommittee on Investigations, Oversight and Regulations
United States House Small Business Subcommittee on Economic Growth, Tax and Capital Access

United States Senate Committee on Small Business and Entrepreneurship

United States Senate Committee on Small Business and Entrepreneurship
The U.S. Senate Committee on Small Business and Entrepreneurship is a standing committee of the United States Senate. It has jurisdiction over the Small Business Administration and is also charged with researching and investigating all problems of American small business enterprises.
Jaap de Wilde
Jacobus Hubertus "Jaap" de Wilde (born 17 May 1957) is a Dutch academic. A native of Zuidlaren, he has been a Professor of International Relations and Security Studies at the University of Groningen since 2007. He headed the department of International Relations between 2008 and 2012. From 2001 to 2007 he was professor in European Security Studies at the Department of Political Sciences, VU University Amsterdam, and from 1995–2007 he was senior research fellow in European Studies and IR Theory at the Centre for European Studies (CES), University of Twente. From 1993–1995 he worked at the Copenhagen Peace Research Institute (COPRI).

University of Groningen
The University of Groningen (abbreviated as UG; Dutch: Rijksuniversiteit Groningen, abbreviated as RUG) is a public research university of more than 30,000 students in the city of Groningen, Netherlands. Founded in 1614, the university is the second oldest in the country (after Leiden).

The University of Groningen has eleven faculties, nine graduate schools, 27 research centres and institutes, and more than 175-degree programmes. The university's alumni and faculty include Johann Bernoulli, Aletta Jacobs, four Nobel Prize winners, nine Spinoza Prize winners, one Stevin Prize winner, various members of the Dutch royal family, several politicians, the first president of the European Central Bank, and a secretary general of NATO.
Edward J. Keyes
Edward J. Keyes (January 29, 1859 – May 10, 1929) was an American farmer and politician.

Born in the town of Lyndon, Sheboygan County, Wisconsin. Keyes was a farmer, in the town of Lyndon, and owned a cheese factory. He also worked for the I. L. Wood Barbed Wire Fence Manufacturing Company and worked on a farm for two years in DeKalb, Illinois. Keyes served as chairman of the Lyndon Town Board and was a Republican. He served in the Wisconsin State Assembly in 1907 and 1909. Keyes died near Plymouth, Wisconsin after a long illness.

Sheboygan County, Wisconsin
Sheboygan County (/ʃɪˈbɔɪɡən/ ⓘ) is a county in the U.S. state of Wisconsin. It is named after the Sheboygan River. As of the 2020 census, the population was 118,034. Its county seat is Sheboygan. The county was created in 1836 and organized in 1846. At the time, it was located in the Wisconsin Territory. Sheboygan County comprises the Sheboygan, WI Metropolitan Statistical Area. Part of the Holyland region is located in northwestern Sheboygan County.
Immirzi parameter
The Immirzi parameter (also known as the Barbero–Immirzi parameter) is a numerical coefficient appearing in loop quantum gravity (LQG), a nonperturbative theory of quantum gravity. The Immirzi parameter measures the size of the quantum of area in Planck units. As a result, its value is currently fixed by matching the semiclassical black hole entropy, as calculated by Stephen Hawking, and the counting of microstates in loop quantum gravity.

Volume operator
A quantum field theory of general relativity provides operators that measure the geometry of spacetime. The volume operator  of a region  is defined as the operator that yields the expectation value of a volume measurement of the region , given a state  of quantum General Relativity. I.e. is the expectation value for the volume of . Loop Quantum Gravity, for example, provides volume operators, area operators and length operators for regions, surfaces and path respectively.
A Case for the Blues
A Case for the Blues is a blues album by Katmandu, a British band made up of successful musicians from differing musical backgrounds, including Peter Green of Fleetwood Mac, Ray Dorset of Mungo Jerry and Vincent Crane of Atomic Rooster. Released in 1985, this was the only album by the band.

A Case for the Blues has been re-released several times, sometimes as a Peter Green solo album, such as the 1987 release on the Original Masters label. Other releases credit the album to Peter Green and Friends.

Mungo Jerry
Mungo Jerry (formerly known as Mungo Jerry Blues Band) are a British rock band formed by Ray Dorset in Ashford, Middlesex, in 1970. Experiencing their greatest success in the early 1970s, with a changing line-up always fronted by Dorset, the group's biggest hit was "In the Summertime", which sold 8–16 million copies worldwide. They had nine charting singles in the UK, including two number ones, five top-20 hits in South Africa, and four in the Top 100 in Canada.
Vilalba dels Arcs
Vilalba dels Arcs (Catalan pronunciation: [biˈlalβa ðelz ˈaɾks]) is a municipality in the comarca of Terra Alta in Catalonia, Spain. It has a population of 608 (register office, 2024) .

This town is located in a wine-producing area. The area suffered much during the Battle of the Ebro. At the site known as Els Barrancs there are still almost intact trenches of the Spanish Republican line of defence, part of a long defensive line built between Vilalba dels Arcs and La Pobla de Massaluca.

Terra Alta (comarca)
Terra Alta (Western Catalan: [ˈtɛra ˈalta]) is a sparsely populated inland comarca (county) in Terres de l'Ebre, Catalonia (Spain). Its capital is Gandesa. It is also known as Castellania, a name dating back to its medieval status as a fiefdom held by the Order of Knights of the Hospital of St. John of Jerusalem under the Crown of Aragon.
Julia Ivonchyk
Julia Ivonchyk (née Kovalenko, Belarusian: Юлія Каваленка, born 27 July 1994) is a Belarusian female acrobatic gymnast. With partners Angelina Sandovich and Yuliya Ramanenka, Kovalenko achieved 5th in the 2014 Acrobatic Gymnastics World Championships.

At the 2013 World Games, she won a bronze medal in the group event.

At the 2017 World Games, she won a silver medal in the women's group all-around event.

At the 2017 Acrobatic Gymnastics European Championships, she won bronze medals in three women's group events: all-around, balance, and dynamic.

At the 2018 Acrobatic Gymnastics World Championships, she won a bronze medal in the team event.

2017 World Games
The 2017 World Games (Polish: Igrzyska Światowe 2017), also known as Wrocław 2017, was the tenth edition of the World Games, held from 20 to 30 July 2017 in Wrocław, Poland. The World Games were organized by the Wrocław Organizing Committee. Wrocław was selected as the host city in January 2012 in Lausanne, over Budapest, Hungary. It was the first time The World Games was organised in Poland.

Wrocław was the sixth city in Europe after London (1985), Karlsruhe (1989), The Hague (1993), Lahti (1997) and Duisburg (2005) to host The World Games.

A total of 201 events in 27 official sport disciplines were held during the Games. This is the first time that floorball, women's lacrosse, and Muay Thai have been included in The World Games as official sports. Also, a total of 21 events in 4 invitational sports, American football, indoor rowing, kickboxing, and motorcycle speedway were held during the Games.
Soul Dressing
Soul Dressing is the second album by the Southern soul band Booker T. & the M.G.'s, released in 1965. It was their final album with bassist Lewie Steinberg, who was replaced by Donald "Duck" Dunn.

The title track peaked at No. 95 on the Billboard Hot 100.

Al Jackson Jr.
Albert J. Jackson Jr. (November 27, 1935 – October 1, 1975) was an American drummer, producer, and songwriter. He was a founding member of Booker T. & the M.G.'s, a group of session musicians who worked for Stax Records and produced their own instrumentals. Jackson was affectionately dubbed "The Human Timekeeper" for his drumming ability. He was posthumously inducted into the Memphis Music Hall of Fame in 2015, and the Rock and Roll Hall of Fame as a member of Booker T. & the M.G.'s in 1992.
Karl Luik
Karl Julius Luik (12 July 1883 in Koikküla Parish (now Valga Parish), Kreis Werro – 5 March 1948 in Tobolsk, Russia) was an Estonian politician. He was a member of Estonian National Assembly (Estonian: Rahvuskogu) and Mayor of Tartu from 1920 until 1934.

Võru kreis
Werro County (German: Kreis Werro, Estonian: Võru kreis, Russian: Верроскій уѣздъ, romanized: Verroskiy uyezd) was one of the nine subdivisions of the Governorate of Livonia of the Russian Empire. It was situated in the northeastern part of the governorate (in present-day southeastern Estonia). Its capital was Võru (Werro). The territory of Kreis Werro corresponds to the present-day Võru County, most of Põlva County and parts of Valga County.
Brigade Speciale Beveiligingsopdrachten
The Brigade Speciale Beveiligingsopdrachten (BSB) (Special Security Missions Brigade) is the elite police tactical unit of the Royal Netherlands Marechaussee. Its missions include counter-terrorism, protection of government and military officials, and targeting organised crime.

Like many other European police tactical units, the BSB was established in 1975 following the Munich massacre. The unit was modeled after the GSG 9. Although the BSB conducts special operations, its missions are not planned by the Netherlands Special Operations Command (NLD SOCOM).

Soesterberg Air Base
Soesterberg Air Base (IATA: UTC, ICAO: EHSB) was a Royal Netherlands Air Force (RNLAF) military air base located in Soesterberg, 14 kilometres (8.7 mi) east-northeast of Utrecht.  It was first established as an airfield in 1911, and in 1913, the Dutch Army bought the field and established the Army Aviation Division.

For almost 40 years, United States Air Force facilities at Soesterberg, named Camp New Amsterdam, were a major front line USAFE air base during the Cold War.  The base was closed on 31 December 2008, due to budget cuts in the Dutch armed forces.  The air base ceased flying operations on 12 November 2008, when the command was transferred from the RNLAF to the Ministry of Defence which will maintain the base until it will be given back to nature.  The last fighter ever to depart, delayed due bad weather at Aviano AB, was a Greek F-4E Phantom II.  The former USAFE facilities remained in military hands, and will now officially be called Camp New Amsterdam.
Zhao Yun
Zhao Yun (Chinese: 趙雲 pronunciationⓘ) (died 229), courtesy name Zilong (子龍), was a military general who lived during the late Eastern Han dynasty and early Three Kingdoms period of China. Originally a subordinate of the northern warlord Gongsun Zan, Zhao Yun later came to serve another warlord, Liu Bei, and had since accompanied him on most of his military exploits, from the Battle of Changban (208) to the Hanzhong Campaign (217–219). He continued serving in the state of Shu Han – founded by Liu Bei in 221 – in the Three Kingdoms period and participated in the first of the Northern Expeditions until his death in 229. While many facts about Zhao Yun's life remain unclear due to limited information in historical sources, some aspects and activities in his life have been dramatised or exaggerated in folklore and fiction. In the 14th-century historical novel Romance of the Three Kingdoms, he was lauded as a member of the Five Tiger Generals under Liu Bei.

Yizhou (Southwest China)
Yizhou (益州), Yi Province or Yi Prefecture, was a zhou (province) of ancient China. Its capital city was Chengdu. During the Han dynasty, it included the commanderies Hanzhong, Ba, Guanghan, Shu, Wenshan, Jianwei, Zangke, Yuexi, Yizhou and Yongchang. It was bordered in the north by Liang Province and Yong Province. At its greatest extent, Yi covered present-day central and eastern Sichuan, Chongqing, southern Shaanxi and parts of Yunnan and Guizhou.
2021 Epsom Derby
The 2021 Epsom Derby was the 242nd annual running of the Derby horse race and took place at Epsom Downs Racecourse on 5 June 2021. The race was sponsored for the first time by the online car-dealer Cazoo.

The winner was Godolphin's bay colt Adayar, ridden by Adam Kirby and trained at Newmarket by Charlie Appleby. Godolphin and Appleby were winning the race for the second time, having taken the prize with Masar in 2018.

Epsom Downs Racecourse
Epsom Downs is a Grade 1 racecourse in a hilly area near Epsom in Surrey, England which is used for thoroughbred horse racing. The "Downs" referred to in the name are part of the North Downs.

The course has a crowd capacity of 130,000 including people watching from the Epsom Downs, an area freely open to the public. The course is best known for hosting the Derby Stakes, which has come to be widely referred to as The Derby or as the Cazoo Derby for sponsorship reasons, the United Kingdom's premier thoroughbred horse race for three-year-old colts and fillies, over a mile and a half (2400 m). It also hosts the Oaks Stakes (also widely referred to as The Oaks) for three-year-old fillies, and the Coronation Cup for horses aged four years and upwards. All three races are Group 1 races and run over the same course and distance.

The Chairman of the course since 2022 is Brian Finch.  The course is operated by the Jockey Club.  Queen Elizabeth II attended the Derby in most years of her reign.
Erik Karlsson
Erik Sven Gunnar Karlsson (pronounced [ˈêːrɪk ˈkɑ̌ːɭsɔn]; born 31 May 1990) is a Swedish professional ice hockey player who is a defenceman for the Pittsburgh Penguins of the National Hockey League (NHL). Karlsson was drafted in the first round, 15th overall, by the Ottawa Senators at the 2008 NHL entry draft, with whom he spent his first nine NHL seasons; he has also played for the San Jose Sharks. Karlsson is a three-time winner of the James Norris Memorial Trophy as the NHL's best defenceman, winning the award in 2012, 2015, and 2023.

Winnipeg Jets
The Winnipeg Jets are a professional ice hockey team based in Winnipeg. The Jets compete in the National Hockey League (NHL) as a member of the Central Division in the Western Conference. The team is owned by True North Sports & Entertainment, playing its home games at Canada Life Centre.

The franchise was established as the Atlanta Thrashers on June 25, 1997, and began play in the 1999–2000 NHL season. True North Sports & Entertainment then bought the team in May 2011, and relocated the Thrashers to Winnipeg prior to the 2011–12 season, making them the first NHL franchise to relocate since the Hartford Whalers became the Carolina Hurricanes in 1997. The team was renamed the Jets after Winnipeg's original WHA/NHL team, which relocated after the 1995–96 season due to financial issues to become the now-inactive Phoenix (later Arizona) Coyotes.