OpenLLM-France/wikimedia huggingface dataset:
# Carathéodory's criterion

Carathéodory's criterion is a result in measure theory that was formulated by Greek mathematician Constantin Carathéodory that characterizes when a set is Lebesgue measurable.

## Statement

Carathéodory's criterion: Let $\lambda ^{*}:{\mathcal {P}}(\mathbb {R} ^{n})\to [0,\infty ]$ denote the Lebesgue outer measure on $\mathbb {R} ^{n},$ where ${\mathcal {P}}(\mathbb {R} ^{n})$ denotes the power set of $\mathbb {R} ^{n},$ and let $M\subseteq \mathbb {R} ^{n}.$ Then $M$ is Lebesgue measurable if and only if $\lambda ^{*}(S)=\lambda ^{*}(S\cap M)+\lambda ^{*}\left(S\cap M^{c}\right)$ for every $S\subseteq \mathbb {R} ^{n},$ where $M^{c}$ denotes the complement of $M.$ Notice that $S$ is not required to be a measurable set.

## Generalization

The Carathéodory criterion is of considerable importance because, in contrast to Lebesgue's original formulation of measurability, which relies on certain topological properties of $\mathbb {R} ,$ this criterion readily generalizes to a characterization of measurability in abstract spaces. Indeed, in the generalization to abstract measures, this theorem is sometimes extended to a definition of measurability. Thus, we have the following definition: If $\mu ^{*}:{\mathcal {P}}(\Omega )\to [0,\infty ]$ is an outer measure on a set $\Omega ,$ where ${\mathcal {P}}(\Omega )$ denotes the power set of $\Omega ,$ then a subset $M\subseteq \Omega$ is called $\mu ^{*}$–measurable or Carathéodory-measurable if for every $S\subseteq \Omega ,$ the equality$\mu ^{*}(S)=\mu ^{*}(S\cap M)+\mu ^{*}\left(S\cap M^{c}\right)$holds where $M^{c}:=\Omega \setminus M$ is the complement of $M.$
The family of all $\mu ^{*}$–measurable subsets is a σ-algebra (so for instance, the complement of a $\mu ^{*}$–measurable set is $\mu ^{*}$–measurable, and the same is true of countable intersections and unions of $\mu ^{*}$–measurable sets) and the restriction of the outer measure $\mu ^{*}$ to this family is a measure.
# Canton of Péronnas

The canton of Péronnas is a former administrative division in eastern France. It was disbanded following the French canton reorganisation which came into effect in March 2015. It had 14,371 inhabitants (2012).
The canton comprised 8 communes:
* Lent
* Montagnat
* Montracol
* Péronnas
* Saint-André-sur-Vieux-Jonc
* Saint-Just
* Saint-Rémy
* Servas

## Demographics

Historical population of Canton of Péronnas (Source: INSEE) :
| Year | 1962 | 1968 | 1975 | 1982 | 1990 | 1999 |
| Population | 4 598 | 5 394 | 7 096 | 9 837 | 11 259 | 12 200 |
| From the year 1962 on: No double counting—residents of multiple communes (e.g. students and military personnel) are counted only once. |||||||
# Carbinoxamine/pseudoephedrine

Carbinoxamine/pseudoephedrine is an antihistamine and decongestant combination, marketed as Rondec, Ceron and Coldec. It contains two active ingredients: carbinoxamine and pseudoephedrine.
# For Girls Who Grow Plump in the Night

Professional ratings :
| Review scores ||
| Source | Rating |
| AllMusic | |
For Girls Who Grow Plump in the Night is the fifth studio album released by the Canterbury scene band Caravan. Richard Sinclair and Steve Miller left the band prior to the recording of this album. They were replaced by John G. Perry and the returning Dave Sinclair. Viola player Geoff Richardson was added to the band.

## Track listing

All songs composed by Pye Hastings, except where noted.

### Side two

The following bonus tracks were included on the 2001 remastered edition of the CD.

## Personnel
### Caravan

* Pye Hastings – electric and acoustic guitars, lead vocals
* Geoff Richardson – viola
* David Sinclair – Hammond organ, piano, electric piano, Davoli synthesizer, ARP synthesizer on (1 b)
* John G. Perry – bass, vocals, percussion
* Richard Coughlan – drums, percussion, timpani

### Additional personnel

* Rupert Hine – ARP synthesizer (1a,b & 6)
* Frank Ricotti – congas ( 1 b, 2, 4, 7)
* Jimmy Hastings – flute (1)
* Pete King – flute, alto saxophone (1)
* Harry Klein – clarinet, baritone saxophone (1)
* Tony Coe – clarinet, tenor saxophone (1)
* Henry Lowther – trumpet (1)
* Chris Pyne – trombone (1)
* Barry Robinson – piccolo (1)
* Tom Whittle – clarinet, tenor saxophone (1)
* Jill Pryor – voice (4)
* Paul Buckmaster – electric cello (7)
* Orchestra arranged by John Bell and Martyn Ford, conducted by Martyn Ford

## Releases

| Year | Type | Label | Catalog # |
| 1973 | LP | Deram | SDLR12 |
| 1973 | LP | London | 627 |
| 1991 | CD | Polydor Records | PO 1836 |
| 1999 | CD | Deram | 820971 |
| 2001 remaster | CD | Decca | 8829802 |
| 2001 | CD | Decca | 9060 |
| 2002 | CD | Universal/Island | 2392 |
| 2005 | CD | Universal International | 882980 |
| 2007 | CD | Eclectic Discs | 1303 |
| 2014 | SACD | Universal | UIGY-9545 |
Source:
# Franklin Township, Surry County, North Carolina

Franklin Township is one of fifteen townships in Surry County, North Carolina, United States. The township had a population of 2,130 according to the 2020 census. The township was named for the family of Jesse Franklin, a former governor of North Carolina and resident of the area.
Geographically, Franklin Township occupies 42.7 square miles (111 km$^2$) in northwestern Surry County, with its northern border shared with the state of Virginia. There are no incorporated municipalities within Franklin Township; however, there are several smaller, unincorporated communities located here, including Ladonia and Lowgap. Most of Franklin Township is mountainous and features several of Surry County's most prominent peaks.
36°30′25″N 80°51′56″W﻿ / ﻿36.5069964°N 80.8654534°W﻿ / 36.5069964; -80.8654534
* This article about a location in Surry County, North Carolina is a stub. You can help Wikipedia by expanding it.
* v
* t
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# Franklin Township, Lee County, Iowa

Franklin Township is a township in Lee County, Iowa, in the United States.

## History

Franklin Township was organized in 1841.
# Franklin Township, Miller County, Missouri

Franklin Township is an inactive township in Miller County, in the U.S. state of Missouri.
Franklin Township was established in 1860, and named after the local Franklin family.
# Castle Rock, Wisconsin

Castle Rock is a town in Grant County, Wisconsin, United States. The population was 314 at the 2000 census. The unincorporated community of Castle Rock is located in the town.

## Geography

According to the United States Census Bureau, the town has a total area of 35.8 square miles (92.7 km$^2$), all of it land.

## Demographics

At the 2000 census there were 314 people, 112 households, and 86 families living in the town. The population density was 8.8 people per square mile (3.4/km$^2$). There were 122 housing units at an average density of 3.4 per square mile (1.3/km$^2$). The racial makeup of the town was 97.77% White, 0.32% Native American, 0.32% from other races, and 1.59% from two or more races. Hispanic or Latino of any race were 0.64%.
Of the 112 households 36.6% had children under the age of 18 living with them, 66.1% were married couples living together, 4.5% had a female householder with no husband present, and 23.2% were non-families. 17.9% of households were one person and 5.4% were one person aged 65 or older. The average household size was 2.80 and the average family size was 3.14.
The age distribution was 25.8% under the age of 18, 6.1% from 18 to 24, 27.7% from 25 to 44, 25.8% from 45 to 64, and 14.6% 65 or older. The median age was 40 years. For every 100 females, there were 97.5 males. For every 100 females age 18 and over, there were 108.0 males.
The median household income was $40,000 and the median family income was $44,286. Males had a median income of $18,750 versus $19,792 for females. The per capita income for the town was $16,201. About 2.2% of families and 3.0% of the population were below the poverty line, including none of those under age 18 and 8.5% of those age 65 or over.
# Frans Menton

Fransoys or Frans Menton (c.1550–1615) was a Dutch Golden Age portrait painter.

## Biography

Little is known of his early life, but according to Van Mander in 1604, he spoke with him about his training as a pupil of Frans Floris in his workshop in Antwerp. Apparently that is where Menton received much of his training. Van Mander based his list of Frans Floris pupils on Menton's information. Of Menton himself, Van Mander stated that he was a good portrait painter and engraver. Houbraken repeated Van Mander's comment and added that his gravestone in Alkmaar gave his death date as March 24, 1615.
The Stedelijk Museum Alkmaar has two militia pieces by him on display.
According to the RKD he signed his works with the monogram F.ME..
# Catahoula Parish Courthouse

The Catahoula Parish Courthouse, located at 301 Bushley Street (LA 124) in Harrisonburg, Louisiana, was built in 1930. It was listed on the National Register of Historic Places in 1988.
It is a four-story Classical Revival building "with a strong rusticated base and a colossal piano nobile composed of engaged Ionic columns." It is asserted in its 1988 NRHP nomination that "The Catahoula Parish Courthouse is architecturally significant on the local level as the grand landmark of the parish."
# Catharina Halkes

Catharina Joanna Maria Halkes (Vlaardingen, 2 July 1920 - Nijmegen, 21 April 2011) was a Dutch theologian and feminist, notable for having been the first Dutch professor of feminism and Christianity, at the Radboud University Nijmegen from 1983 to 1986. A Roman Catholic who was originally schooled in Dutch language and literature, she became active in the women's movement within the church, and gained a measure of notoriety when she was forbidden to address Pope John Paul II during his visit to the Netherlands in 1985. She is considered the founding mother of feminist theology in the Netherlands.

## Accomplishments

Halkes was the first professor of Feminism and Christianity at Radboud University in The Netherlands, which was then known as the Catholic University of Nijmegen.
# Franklin Township, Adams County, Ohio

Franklin Township is one of the fifteen townships of Adams County, Ohio, United States. The population was 1,097 at the 2020 census.

## Geography

Located in the northeastern corner of the county, it borders the following townships:
* Mifflin Township, Pike County - north
* Sunfish Township, Pike County - northeast
* Rarden Township, Scioto County - east
* Meigs Township - south
* Bratton Township - west
* Brushcreek Township, Highland County - northwest corner
No municipalities are located in Franklin Township.

## History

Franklin Township was organized in 1828. It is named for Benjamin Franklin.
It is one of twenty-one Franklin Townships statewide.

## Government

The township is governed by a three-member board of trustees, who are elected in November of odd-numbered years to a four-year term beginning on the following January 1. Two are elected in the year after the presidential election and one is elected in the year before it. There is also an elected township fiscal officer, who serves a four-year term beginning on April 1 of the year after the election, which is held in November of the year before the presidential election. Vacancies in the fiscal officership or on the board of trustees are filled by the remaining trustees.
# Frank van Straten

Frank Van Straten AM (born 14 May 1936) was an Australian performing arts historian, author and former director of the Performing Arts Museum. He died on 19 April 2024.
Van Straten was the first archivist of the Performing Arts Museum (now Australian Performing Arts Collection), at the Arts Centre Melbourne, and its director from 1984 until 1993.
Between 1986 and 2001, he researched and presented ABC Local Radio's Nostalgia segment, broadcast on Melbourne's 774 and the ABC Victorian Regional Network.
In 2001, Van Straten acted as the Historical Consultant for Graeme Murphy's 'dance musical' Tivoli, performed by the Sydney Dance Company, which premiered at the State Theatre, Arts Centre, Melbourne.
Van Straten served on the board of the National Theatre, Melbourne. He also served on the judging panels of the Green Room Awards and Helpmann Awards. He was a patron of the Cinema and Theatre Historical Society (Victoria), and a founding member and committee member of the Victoria Theatres Trust (now Theatre Heritage Australia).
In 1999, Van Straten received the Medal of the Order of Australia (OAM) in honour of his contributions to the performing arts in Australia.
In 2007, Van Straten was appointed Live Performance Australia's Official Historian.
Van Straten was made a Member of the Order of Australia (AM) in the 2017 Queen's Birthday Honours.
# Frank von Zerneck

Frank von Zerneck (born November 4, 1940) is an American television producer.

## Career

Zerneck's career began as a theater producer in Los Angeles, but moved to television in 1975 in a collaboration with Robert Greenwald through Moonlight Productions, which resulted in the Emmy nominated docudrama 21 Hours at Munich. They briefly partnered with former ABC employee Stu Samuels in the mid to late 1980s. In 1987 Zerneck and fellow producer Robert M. Sertner created von Zerneck/Sertner Films, a long-term venture which has resulted in nearly a hundred television films. Of the company's most notable productions are four Native American films produced for Turner Network Television between 1993 and 1996, which included the Emmy winning Geronimo, Crazy Horse, and Golden Globe nominated Lakota Woman. Tecumseh, which concluded the series, was also critically acclaimed. Recent productions have largely consisted of disaster and true crime dramas.
# Frank van Neck

Frank Lionel Milton van Neck (25 August 1873 – 8 March 1953) was the founder of a firm of manufacturing opticians that later became Peeling and Van Neck, manufacturers of the Van Neck press camera.
Frank van Neck was born in London on 25 August 1873, son of William Grant Neck (1835–1884), a stencil plate engraver, and Louisa Milton (c.1842–1932). He married Annette Rachel Howcroft (1869–1945) in 1899.
He founded Van Neck and Co, manufacturing opticians, around 1897. Their first premises were at 72 Buckingham Gate and 11 Cursiter Street, but by 1910 they had moved to 32 Grays Inn Road. In 1921 they merged with another manufacturing optician, R. E. Peeling, to become Peeling and Van Neck, with workshops at 32 Grays Inn Road and a showroom at 4-6 Holborn Circus.
Peeling and Van Neck Limited of 4-6 Holborn Circus imported photographic and cinematographic cameras, projectors, film and equipment, especially Goerz. In 1927, The Times reported that real advances had been made in colour photography by Messrs. Van Neck and Co in their transparencies made on “Lignosa” [or Lignose] natural colour film packs and roll films, which pre-dated Kodachrome and Agfacolor. The firm was best known for its portable Van Neck press camera which became widely used by press photographers until the 1950s.
The firm remained at Holborn Circus until around 1955, later moving to 79 Turnmill Street and then 120 Albert Street. There is no connection between Frank van Neck and the 1890s Belgian camera maker, Louis Van Neck. Frank van Neck of Norman Cottage, Cookham, died in hospital at Maidenhead on 8 March 1953, leaving £15,634.
# Catephia triphaenoides

Catephia triphaenoides is a species of moth of the family Erebidae. It is found in Madagascar.
# Castries Comprehensive Secondary School

Castries Comprehensive Secondary School is a secondary school located in Vide Bouteille, Castries, Saint Lucia.
The school opened in 1974. It was donated by the Canadian government.

## Notable alumni

* Sarah Flood-Beaubrun, former Minister of Home Affairs
* Lenard Montoute, Minister of Youth and Sports and MP for Gros Islet (2006–2011)
# Fred Gleave

Frederick "Fred" Gleave was an English professional rugby league footballer who played in the 1900s and 1910s. He played at representative level for England, and at club level for Wigan, as a stand-off.

## Playing career
### International honours

Fred Gleave won a cap for England while at Wigan in 1913 against Wales.

### County Cup Final appearances

Fred Gleave played scrum-half in Wigan's 10-9 victory over Oldham in the 1908 Lancashire Cup Final during the 1908–09 season at Wheater's Field, Broughton, on Saturday 19 December 1908, and played stand-off in the 21–5 victory over Rochdale Hornets in the 1912 Lancashire Cup final during the 1912–13 season at Weaste, Salford, on Wednesday 11 December 1912.
# Catachlorops rufescens

Catachlorops rufescens is a species of biting horse-fly in the family Tabanidae.

## Taxonomy

Catachlorops rufescens was described by Johan Christian Fabricius in 1805.

## Description

The adult body size of C. rufescens averages around 11 mm (0.43 in), while the wing length averages around 10 mm (0.39 in). The eyes are a solid green in color. The overall body coloration is mostly dark brown to black, including the legs. On the thorax, the postpronotal lobe is yellow, its setae yellow as well; Scutum is a reddish brown with notably dense gray pruinescence in the anterior region; the scutellum is light gray. C. rufescens has a broad dark brown abdomen with white setae on tergites I-IV in the middle. On the wings there is a dark circle-like pigmentation going from the pterostigma to cell r5, down to the middle of m3. The costal margin of the wings have slight pigmentation, while the rest of the wings are hyaline for the most part.

## Distribution and habitat

Catachlorops rufescens is endemic to the tropical lowland region of the Amazon rainforest and can be found Guyana, French Guiana, and northern parts of Brazil. Larvae can be found in freshwater watercourses, such as streams, around underwater roots.
# Caucasus (Fabergé egg)

The Caucasus Egg is a jewelled enameled Easter egg made by Michael Perkhin under the supervision of the Russian jeweller Peter Carl Fabergé in 1893. The Fabergé egg was made for Alexander III of Russia, who presented it to his wife, Empress Maria Feodorovna.
Currently the egg is a long term installation at the Metropolitan Museum of Art in New York City, New York, as part of the Matilda Geddings Gray Foundation.

## Design

The egg is made of yellow and varicoloured gold, silver, ruby enamel, rose-cut diamonds, portrait diamonds, platinum, ivory, pearls, rock crystal and watercolour on ivory.
It commemorates Abastumani in Caucasus (Georgia) where Grand Duke George spent most of his life after being diagnosed with tuberculosis. Miniatures were done and signed by Krijitski. The miniatures are revealed by opening four pearl-bordered doors around the egg. Each door bears a diamond-set numeral of the year, forming the year 1893. Behind the hinged cover at the top is a portrait of the Grand Duke in his naval uniform.
This is the first Imperial egg known to be dated. Ruby red enamel was used only one other time for the Imperial eggs.

## Surprise

The surprise for this egg are the miniature paintings themselves.
# Catherine O'Neill (athlete)

Catherine O'Neill born 4 December 1975) is a former Paralympian athlete from Ireland who competed mainly in category F51 track and field events.

## Athletics career

O'Neil took up disability sport whilst at a sports camp in New York City at the age of twelve. She first represented Ireland at a major international tournament at Birmingham during the 1998 IPC Athletics World Championships, winning gold in the F51 women's discus throw. O'Neil competed at three Summer Paralympic Games during her career, starting at the 2000 Summer Paralympics at Sydney. Initially specializing in the discus, show progressed in her later career to also entering club throw events. Although not competing in Athens, O'Neill was in the Ireland team for both the 2008 Games in Beijing and 2012 Games in London. Her only Paralympic podium finish came at London, where she won a silver in the discus throw – F51/52/53.
O'Neill's most successful tournament was the 2011 IPC Athletics World Championships in Christchurch, winning a gold in the discus throw and a silver in the club throw. After the 2014 IPC Athletics European Championships at Swansea, O'Neill decided to retire from sport.
# Catherine O'Flynn

Catherine O'Flynn (born 1970) is a British writer. She has published three novels for adults, and two for children as well as various articles and short stories. Her debut novel, What Was Lost, won the prestigious first novel prize at the Costa Book Awards in 2008.

## Biography

Prior to the publication of What Was Lost she worked in a variety of jobs including deputy manager of a large record shop, post woman, web editor, teacher and mystery shopper. After spending some time in and around Barcelona, she now lives and works in Birmingham, England. She is married to Peter Fletcher, and they have two daughters.
Her first novel, What Was Lost, was published in January 2007. This novel received critical acclaim as an examination of the often lacklustre and empty experience of modern life, contrasted with the energy and optimism of a young girl who went missing in the mid-1980s. What Was Lost was long listed for the 2007 Man Booker Prize for Fiction and the Orange Prize for Fiction, and shortlisted for the Guardian First Book Award. It won the Jelf Group First Novel Award at the Guildford Book Festival and the prestigious First Novel prize at the Costa Book Awards in January 2008. In April 2008 she was named Newcomer of the Year at the Galaxy British Book Awards.
Her second book, The News Where You Are was published on 1 July 2010 and launched the following day at Ikon Gallery in Birmingham. It features the tale of a disenchanted local TV news anchor, who becomes obsessed with the unheralded deaths that he is routinely required to report as part of his day job. One of the stories he follows up has a curious connection to his own life and his seemingly ageless predecessor. O'Flynn was praised for being in this novel the "mistress of compassion" and "the JG Ballard of Birmingham...finding poetry and meaning where others see merely boredom and dereliction".
Her third book, Mr. Lynch's Holiday, was published on 1 August 2013, and tells the story of an estranged father and son, both emigrants from their respective homelands, but for very different reasons. Meeting up in an unfinished (but largely abandoned) housing development in Spain, both are in search of a connection with themselves and each other. The novel garnered numerous favourable reviews for its "brilliant wit and warmth", its "rare love story between a father and a son" and its treatment of "the absurdities of the credit boom", "excelling in exploring the strangeness of being the outsider and the stories people tell themselves to survive".
In 2011 she contributed a short story "The Stickiness of Lime Trees" to an anthology supporting The Woodland Trust. The anthology - Why Willows Weep - has so far helped The Woodland Trust plant approximately 50,000 trees, and is to be re-released in paperback format in 2016.
# Catalpic acid

Catalpic acid is a conjugated polyunsaturated fatty acid. The melting point of this fatty acid is 32 °C. Catalpic acid occurs naturally in the seeds of yellow catalpa (Catalpa ovata) and southern catalpa (Catalpa bignonioides). Seeds of Catalpa species contain about 40% catalpic acid.