hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Proofs of convergence of random variables
This article is supplemental for “Convergence of random variables” and provides proofs for selected results.

Several results will be established using the portmanteau lemma: A sequence {Xn} converges in distribution to X if and only if any of the following conditions are met:

for all bounded, continuous functions ;

for all bounded, Lipschitz functions ;

for all closed sets ;

Closed set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit points. In a complete metric space, a closed set is a set which is closed under the limit operation. This should not be confused with closed manifold.

Sets that are both open and closed are called clopen sets.
Acorn Network Computer
The Acorn Network Computer was a network computer (a type of thin client) designed and manufactured by Acorn Computers Ltd. It was the implementation of the Network Computer Reference Profile that Oracle Corporation commissioned Acorn to specify for network computers (for more detail on the history, see Acorn's Network Computer). Sophie Wilson of Acorn led the effort. It was launched in August 1996.

The NCOS operating system used in this first implementation was based on RISC OS and ran on ARM hardware.  Manufacturing obligations were achieved through a contract with Fujitsu subsidiary D2D.

In 1997, Acorn offered its designs at no cost to licensees of RISC OS.

NCOS
NCOS is the graphical user interface-based operating system developed for use in Oracle Corporation's Network Computers, which are discontinued. It was adapted by Acorn Computers from its own RISC OS, which was originally developed for their range of Archimedes desktop computers. It shares with RISC OS the same 4 MB ROM size and suitability for use with TV displays.

In 1999, Pace acquired the set-top box (STB) division of Acorn Computers,: 5 : 9  this being a component in the disposal of assets around the takeover of Acorn by MSDW Investment Holdings. This gave Pace the rights to use and develop NCOS. RISCOS Ltd later announced Embedded RISC OS, which was to have similarities with NCOS.
Chongqing–Wanzhou intercity railway
Chongqing–Wanzhou intercity railway is a high speed railway between urban Chongqing and its satellite district of Wanzhou. It is also known at the Yu-Wan Railway, which are abbreviations for Chongqing and Wanzhou. Construction started in December 2012, according to the summarizing and commending meeting of the phase II of "100-day Battle" in Chongqing Liangjiang New Area. It was completed on 29 November 2016 and takes passengers from Chongqing North Railway Station to Wanzhou North railway station in one hour.

This railway forms a smaller section of two larger railway projects, the Chongqing–Xi'an high-speed railway and the Zhengzhou–Wanzhou high-speed railway, extending north and northeast from Wanzhou respectively.

Wanzhou, Chongqing
Wanzhou District (Chinese: 万州区; pinyin: Wànzhōu Qū) is Chongqing's second most populated urban core area on the upper reaches of the Three Gorges of the Yangtze River in China. It is currently governed as a district of Chongqing Municipality, bordering Sichuan to the northwest and Hubei to the southeast. It was formerly known as Wanxian or Wan County (simplified Chinese: 万县; traditional Chinese: 萬縣; pinyin: Wànxiàn). Prior to Chongqing's formation as a direct-controlled municipality, Wanzhou was part of Sichuan province. The urban core of Wanzhou  is 228 km (142 mi) away from Chongqing's city proper.

The characters for "Wanzhou" mean "myriad-prefecture"; which is derived from the phrase "the place where myriad rivers converge and myriad traders gather" (万川毕汇、万商云集). Due to the construction of the Three Gorges Dam, 47% of Wanzhou's old urban area was submerged and had to be relocated.
2010 Côte d'Ivoire Premier Division
The 2010 Côte d'Ivoire Premier Division season was the 50th edition and current of the top-tier competition of Côte d'Ivoire football. The season began on 17 January 2010 and concluded on 5 November 2010. ASEC Mimosas successfully defended their title and captured their 2nd consecutive championship.

ASEC Mimosas
ASEC Mimosas (short for Association Sportive des Employés de Commerce Mimosas; lit. 'Mimosas Commerce Employees' Sporting Association') is an Ivorian professional football club based in Abidjan. The club is also known as ASEC Abidjan, especially in international club competitions. Founded in 1948, they are the most successful side in Ivorian football, having won the Ivorian Premier Division 29 times and the 1998 CAF Champions League. In addition, ASEC's youth academy, known as Académie MimoSifcom, has produced a number of famous players predominantly based in top foreign leagues, including Bonaventure Kalou, Didier Zokora, Emmanuel Eboué, Bakari Koné, Gervinho, Salomon Kalou, Romaric, Boubacar Barry, Didier Ya Konan, Kolo Touré, Yaya Touré and Odilon Kossounou, all of whom have played internationally.
Veja Mate Offshore Wind Farm
Veja Mate is a German 402 MW offshore wind farm in the German Bight of the North Sea about 95 km northwest of Borkum. The wind farm consists of 67 Siemens Wind Power SWT-6.0-154 turbines, each with a 6 MW capacity.

In January 2017, 18 months after the financial close, the first of the turbines started delivering power to the German grid. The last turbine was installed on 25 May 2017, and commissioning activities were completed on 31 May 2017. Construction was completed in less than 23 months after financial close, almost four months ahead of the schedule agreed at financial close.

The EUR 1.9 billion (US$2.1bn) wind farm is owned by Siemens Financial Services and a consortium of European investors.

The power is delivered via the offshore converter station HVDC BorWin2 to the German onshore Diele substation near Weener.

German Bight
The German Bight (German: Deutsche Bucht [ˈdɔʏtʃə ˈbʊxt]; Danish: tyske bugt; Dutch: Duitse bocht [ˈdœytsə ˈbɔxt]); West Frisian: Dútske bocht; North Frisian: Schiisk Bocht; sometimes also the German Bay) is the southeastern bight of the North Sea bounded by the Netherlands and Germany to the south, and Denmark and Germany to the east (the Jutland peninsula). To the north and west it is limited by the Dogger Bank. The Bight contains the Frisian and Danish Islands. The Wadden Sea is approximately ten to twelve kilometres (6 to 10 miles) wide at the location of the German Bight. The Frisian islands and the nearby coastal areas are collectively known as Frisia. The southern portion of the bight is also known as the Heligoland Bight. Between 1949 and 1956 the BBC Sea Area Forecast (Shipping Forecast) used "Heligoland" as the designation for the area now referred to as German Bight.
Hannah Mills (Quaker)
Hannah Mills was a Quaker from Leeds, England, whose treatment and death in 1790 while confined in the York Asylum (now Bootham Park Hospital) is recognised as having led to the development of the York Retreat, which pioneered the moral treatment of mental illness that became a model for progressive practices worldwide.

Mills was admitted as a young widow to the York Asylum on 15 March 1790, suffering from 'melancholy' (what might now be termed clinical depression). At the request of her relatives, local York Quakers tried to visit her but were refused permission on the grounds that she was in private treatment. Mills died there on 29 April 1790. These events shocked the Quakers. William Tuke was enlisted to help develop a more humane alternative and the York Retreat was opened in 1796.

Moral treatment
Moral treatment was an approach to mental disorder based on humane psychosocial care or moral discipline that emerged in the 18th century and came to the fore for much of the 19th century, deriving partly from psychiatry or psychology and partly from religious or moral concerns. The movement is particularly associated with reform and development of the asylum system in Western Europe at that time. It fell into decline as a distinct method by the 20th century, however, due to overcrowding and misuse of asylums and the predominance of biomedical methods. The movement is widely seen as influencing certain areas of psychiatric practice up to the present day. The approach has been praised for freeing sufferers from shackles and barbaric physical treatments, instead considering such things as emotions and social interactions, but has also been criticised for blaming or oppressing individuals according to the standards of a particular social class or religion.
Arzeti Bilbina
Arzeti Bilbina Huzaimi Setiawan (born 4 September 1974) is an Indonesian model, actress and politician of Minangkabau descent who became a member of the 2019–2024 House of Representatives (DPR) of Republic of Indonesia (RI).

House of Representatives (Indonesia)
6°12′37″S 106°48′00″E﻿ / ﻿6.21028°S 106.80000°E﻿ / -6.21028; 106.80000
The House of Representatives of the Republic of Indonesia (Indonesian: Dewan Perwakilan Rakyat Republik Indonesia, Indonesian pronunciation: [ˌdewan pərwaˌkilan ˈraʔjat re'publik indo'nesija], lit. 'People's Representative Council of the Republic of Indonesia', abbr. DPR-RI or simply DPR, Indonesian: [deˈpeɛr]), is one of two elected chambers of the People's Consultative Assembly (MPR), the national legislature of Indonesia. It is considered the lower house, while the Regional Representative Council (DPD) serves as the upper house; while the Indonesian constitution does not explicitly mention the divide, the DPR enjoys more power, privilege, and prestige compared to the DPD.

Members of the DPR are elected through a general election every five years. Currently, there are 580 members; an increase compared to 575 prior to the 2024 elections. Its members are called Members of Parliament (anggota dewan).
1986–87 Harty Cup
The 1986–87 Harty Cup was the 67th staging of the Harty Cup since its establishment in hurling by the Munster Council of Gaelic Athletic Association in 1918. The competition ran from 11 February to 29 March 1987.

North Monastery unsuccessfully defended its title, in the semi-finals, by losing to St Flannan's College.

St Flannan's College won the Harty Cup final, 3–12 to 2–06, on 29 March 1987 at FitzGerald Park in Kilmallock, against Midleton CBS, in what was their second meeting in the final overall and a first meeting since 1944. It was St Flannan's 13th successive Harty Cup title overall and a last Cup title since 1983.

Limerick CBS's Michael Hickey was the top scorer with 4–14.

1985–86 Harty Cup
The 1985–86 Harty Cup was the 66th staging of the Harty Cup since its establishment in hurling by the Munster Council of Gaelic Athletic Association in 1918. The competition ran from 5 February to 23 March 1986.

North Monastery successfully defended its title.

North Monastery won the Harty Cup final, 1–12 to 0–09, on 23 March 1986 at Páirc Uí Chaoimh in Cork, against Midleton CBS, in what was their first ever meeting in the final. It was North Monastery's 18th successive Harty Cup title overall and a second consecutive title.

North Monastery's Tony O'Keeffe was the top scorer with 1-23.
Mass media in Moldova
The mass media in Moldova refers to mass media outlets based in the Republic of Moldova. Television, magazines, and newspapers are all operated by both state-owned and for-profit corporations which depend on advertising, subscription, and other sales-related revenues. The Constitution of Moldova guarantees freedom of speech.
As a country in transition, Moldova's media system is under transformation.

For the situation in the separatist republic of Transnistria, see Media of Transnistria.

Subscription business model
The subscription business model is a business model in which a customer must pay a recurring price at regular intervals for access to a product or service. The model was pioneered by publishers of books and periodicals in the 17th century. It is particularly common now for digital products, which lend themselves more naturally toward a subscription model.

Subscriptions can be a more convenient, hassle-free transaction for consumers. However, due to inertia among some consumers, they may inadvertently pay for subscriptions that they no longer value because they do not realize that they are subscribed.
Aubin (name)
Aubin is a masculine French given name variant of Albin, from the Roman cognate Albinus, derived from the Latin albus, meaning "white" or "bright". It is also common as a surname. People with the name Aubin include:

Albinus of Angers
Saint Albinus of Angers (French: Saint-Aubin; c. 470 – March 1, 550), also known as Saint Albin (/ˈælbɪn/) in English, was a French abbot and bishop.  Born to a noble Gallo-Roman family at Vannes, Brittany, St. Albinus was a monk and from 504 A.D. Abbot of Tintillac (which no longer stands; its location has not been satisfactorily identified).  His reputation spread during the twenty-five years in which he served as abbot. In 529, St. Albinus was elected, against his wishes, Bishop of Angers.
Romania at the 1984 Summer Olympics
Romania competed at the 1984 Summer Olympics in Los Angeles, United States. 124 competitors, 71 men and 53 women, took part in 86 events in 13 sports. Notably, Romania was the only Eastern Bloc nation to participate at these Games; all others followed the Soviet Union's boycott of the Games. The Romanian athletes were greeted with warm applause and even a standing ovation from the spectators as they entered the Los Angeles Memorial Coliseum during the opening ceremony, in part an affirmation of the nation's defiance of the boycott. The Romanian Olympic team was phenomenally successful at the games, ultimately placing second to the United States in the gold medal tally.

Marin Mustață
Marin Mustață (3 March 1954 – 2007) was a Romanian sabre fencer. He competed at the 1976, 1980 and 1984 Olympics and won team bronze medals in 1976 and 1984. After retiring from competition he worked as a fencing coach with Tractorul Brasov and the Romanian national team. He teamed with his cousin Cornel Marin who is also a sabre fencer.

In 2007, he died of lung cancer.
Campbell Fighting Camels women's basketball
The Campbell Fighting Camels women's basketball team is the women's basketball team that represent the Campbell University in Buies Creek, North Carolina. The school's team currently competes in the Coastal Athletic Association (CAA), having moved from the Big South Conference in 2023.

Buies Creek, North Carolina
Buies Creek (/ˈbuːiːz/ BOO-eez) is a census-designated place (CDP) located in the Neills Creek Township of Harnett County, North Carolina, United States. It is the home of Campbell University. The population was 3,253 at the 2020 census, up from 2,942 in 2010. Buies Creek is a part of the Dunn Micropolitan Area, which is also a part of the greater Raleigh–Durham–Cary Combined Statistical Area (CSA) as defined by the United States Census Bureau.
Elias Karvonen
Elias Karvonen (born July 28, 1994) is a Finnish professional ice hockey forward currently playing for TPS in the Liiga.

Karvonen began playing for TPS through junior setup in 2010 and made his debut for the senior team during the 2014-15 Liiga season. He also had a brief loan spell with TUTO Hockey of Mestis during the 2016-17 season.

Mestis
Mestis (from Finnish: Mestaruussarja, meaning 'Championship series', stylized as MEST1S) is the second-highest men's ice hockey league in Finland. The league was established by the Finnish Ice Hockey Association in 2000 to replace the I-divisioona ('First Division').

Promotion to the SM-liiga is achievable for a Mestis team if it defeats an SM-liiga club in the qualification series and meets all the criteria established by the SM-liiga. However, Mestis is an open league that allows for relegation and promotion with the third league, Suomi-sarja.

Mestis is also the highest league under the governance of the FIHA.
Kent County, New Brunswick
Kent County (2021 population 32,169) is located in east-central New Brunswick, Canada. The county features a unique blend of cultures including Mi'kmaq, Acadian, and English. Some larger tourist attractions include the dune de Bouctouche, Kouchibouguac National Park, and Bonar Law Commons.

Federally, it is split between the ridings of Beauséjour, represented by Dominic LeBlanc of the Liberal Party of Canada and Miramichi—Grand Lake, represented by Jake Stewart of the Conservative Party of Canada. Provincially, it is split between the electoral districts of Kent North and Kent South.

Kent South
Kent South (French: Kent-Sud) was a provincial electoral district for the Legislative Assembly of New Brunswick, Canada.

It was originally created in 1973 with the southern third of Kent County, centered primarily around the town of Bouctouche. It was largely unchanged in the 1994 redistribution. In 2006 it lost the Bouctouche area to Kent.  In the 2013 redistribution its northern half was merged with the southern half of Kent, causing it to regain Bouctouche and add several rural areas to its north, but lose much the extreme southern part of Kent County around Cocagne.
John Gilchrist (linguist)
John Borthwick Gilchrist FRSE (19 June 1759 – 9 January 1841) was a Scottish surgeon, linguist, philologist and Indologist. Born and educated in Edinburgh, he spent most of his early career in India, where he made a study of the local languages. In later life, he returned to Britain and lived in Edinburgh and London. In his final years, he moved to Paris, where he died at the age of 81.

He is principally known for his study of the Hindustani language, which led to it being adopted as the lingua franca of northern India (including present-day Pakistan) by British colonists and indigenous people. He compiled and authored An English-Hindustani Dictionary, A Grammar of the Hindoostanee Language, The Oriental Linguist, and many more. His lexicon of Hindustani was published in Arabic script, Nāgarī script, and in Roman transliteration. He is also known for his role in the foundation of University College London and for endowing the Gilchrist Educational Trust.

Lexicon
A lexicon (pl. lexicons, rarely lexica) is the vocabulary of a language or branch of knowledge (such as nautical or medical).  In linguistics, a lexicon is a language's inventory of lexemes. The word lexicon derives from Greek word λεξικόν (lexikon), neuter of λεξικός (lexikos) meaning 'of or for words'.

Linguistic theories generally regard human languages as consisting of two parts: a lexicon, essentially a catalogue of a language's words (its wordstock); and a grammar, a system of rules which allow for the combination of those words into meaningful sentences. The lexicon is also thought to include bound morphemes, which cannot stand alone as words (such as most affixes). In some analyses, compound words and certain classes of idiomatic expressions, collocations and other phrasemes are also considered to be part of the lexicon. Dictionaries are lists of the lexicon, in alphabetical order, of a given language; usually, however, bound morphemes are not included.
Adolfo Canyon Site
The Adolfo Canyon Site (LA 5665) is an archaeological site containing a Navajo pueblito located in Rio Arriba County, New Mexico, United States. The site is situated on a rock outcrop overlooking Adolfo Canyon. The site consists of a three-room, single story pueblito, and extensive midden area, and six forked stick hogans on the crest of a ridge.

Midden
A midden is an old dump for domestic waste. It may consist of animal bones, human excrement, botanical material, mollusc shells, potsherds, lithics (especially debitage), and other artifacts and biofacts associated with past human occupation.

These features provide a useful resource for archaeologists to study the diets and habits of past societies. Middens with damp, anaerobic conditions can even preserve organic remains in deposits as the debris of daily life are tossed on the pile. Each individual toss will contribute a different mix of materials depending upon the activity associated with that particular toss. During the course of deposition, sediment is deposited as well. Different mechanisms, from wind and water to animal digs, create a matrix which can also be analysed to provide seasonal and climatic information. In some middens individual dumps of material can be discerned and analysed.
Abderrahmane Mehdaoui
Abderrahmane Mehdaoui (7 October 1949 – 13 September 2022) was an Algerian football player and manager who managed the Algeria national team, as well as club sides WA Tlemcen, AGS Mascara and DRB Tadjenanet.

DRB Tadjenanet
Difaa Riadhi Baladiat Tadjenanet (Arabic: الدفاع الرياضي لبلدية تاجنانت), more commonly known as DRB Tadjenanet, was a football club based in Tadjenanet, Algeria. The club was founded in 1971 and its colours were blue and white. Their home stadium, Smaïl Lahoua Stadium, has a capacity of some 9,000 spectators.
Köngen
Köngen is a municipality in the district of Esslingen in Baden-Württemberg in Germany. About nine kilometers from the district city Esslingen am Neckar and about six kilometers away from Nürtingen. It is part of the Stuttgart Region and the European Stuttgart Metropolitan Region.

Eduard Mörike
Eduard Friedrich Mörike (German pronunciation: [ˈeːdu.aʁt ˈfʁiːdʁɪç ˈmøːʁɪkə]; 8 September 1804 – 4 June 1875) was a German Lutheran pastor who was also a Romantic poet and writer of novellas and novels. Many of his poems were set to music and became established folk songs, while others were used by composers Hugo Wolf and Ignaz Lachner in their symphonic works.
Shahine Ezell
Shahine Ezell (Dallas, Texas) is a film and television actor, record producer, talent manager and songwriter. Ezell is Leighton Meester's talent manager as well as the songwriter and record producer of "The Nomads". He attended Booker T. Washington High School for the Performing and Visual Arts and California Institute of the Arts for Acting.

He started his career on the television show Strong Medicine. Then moved on to work on movies: Driftwood (2006 film), Detention, Remember the Daze, and Days of Wrath. He also appeared on the NBC show Crossing Jordan. He now is working on Leighton Meester's debut album.

Days of Wrath (2008 film)
Days of Wrath is a 2008 American drama film starring Jeffrey Dean Morgan, Laurence Fishburne and Wilmer Valderrama. The film is directed by Celia Fox, and written by Mitchell Kapner and Michael Markee.
Extreme Aggression
Extreme Aggression is the fourth studio album by German thrash metal band Kreator released in 1989. While the band had already gained a sizeable following in the US due to their 1988 tour with the crossover thrash band D.R.I., this album introduced many American fans to Kreator, primarily through heavy rotation of the "Betrayer" music video on MTV's Headbangers Ball, which was partly shot at the Acropolis in Athens, Greece. The beginning of the song "Love Us or Hate Us" was used in an early 1990s promo ad by the Los Angeles radio station KNAC. This was their first album issued in the US by Epic Records. The album was also available on picture disc vinyl.

The album's original artwork was that of a man standing in front of a bathroom mirror looking at the reflection of his face falling off, exposing Kreator's mascot demon underneath. However, it was quickly replaced with a new artwork, depicting an image of the band in front of an orange background.

Crossover thrash
Crossover thrash (often abbreviated to crossover) is a fusion genre of thrash metal and hardcore punk. The genre emerged in the mid-1980s, when hardcore punk bands, such as Suicidal Tendencies, Cryptic Slaughter, Corrosion of Conformity and Dirty Rotten Imbeciles, began to incorporate the influence of thrash metal. At this time, the genre was particularly prominent in the New York hardcore scene, where groups including Agnostic Front, Leeway, Cro-Mags and Stormtroopers of Death were widely influential.

The genre largely declined in popularity by the 1990s; however, its influence developed the prominent metalcore genre. Since the 2000s, crossover thrash has experienced a number of underground revivals, which have produced notable acts including Municipal Waste, Trash Talk, Power Trip, and Drain.