In mathematics, specifically in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets. Some authors require additional restrictions on the measure, as described below.
In mathematics, a Borel set is any set in a topological space that can be formed from open sets through the operations of countable union, countable intersection, and relative complement. Borel sets are named after Émile Borel.
In mathematics and in particular measure theory, a measurable function is a function between two measurable spaces such that the preimage of any measurable set is measurable, analogously to the definition that a function between topological spaces is continuous if the preimage of each open set is open. In real analysis, measurable functions are used in the definition of the Lebesgue integral. In probability theory, a measurable function on a probability space is known as a random variable.
In real analysis the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states:
Félix Édouard Justin Émile Borel was a French mathematician and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability.
Armand Borel was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups.
In the theory of algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup. For example, in the group GLn, the subgroup of invertible upper triangular matrices is a Borel subgroup.
George R. Roberts is an American billionaire financier, and one of the three original partners of Kohlberg Kravis Roberts, which he co-founded alongside Jerome Kohlberg and first cousin Henry Kravis in 1976.
Borel is a tiny lunar impact crater located in the southeast part of Mare Serenitatis. It was named after French mathematician Émile Borel. To the northeast is the crater Le Monnier and to the southeast is the crater Abetti. Borel was previously identified as Le Monnier C.
Isabella Dam is an embankment dam located in the Kern River Valley, about halfway down the Kern River course, between the towns of Kernville and Lake Isabella in Kern County, California.
Cleopatra Borel is a female shot putter from Plaisance, Mayaro, Trinidad and Tobago and a 2014 Sportswoman of the Year Award recipient.
Calvin H. Borel is an American jockey in thoroughbred horse racing and rode the victorious mount in the 2007 Kentucky Derby, the 2009 Kentucky Derby and the 2010 Kentucky Derby. His 2009 Derby win with Mine That Bird was the second biggest upset in Derby history, and Borel's winning margin of 6 3⁄4 lengths was the greatest in Derby history since Assault won by 8 lengths in 1946. On May 1, 2009, Borel won the Kentucky Oaks aboard Rachel Alexandra, only the second time since 1993 that a jockey has won the Oaks-Derby combo, and just the seventh time overall a jockey has accomplished this feat in the same year. On May 16, 2009, Borel won the 2009 Preakness Stakes at Pimlico with thoroughbred filly Rachel Alexandra. In doing so, Borel became the first jockey to win the first two jewels of the Triple Crown on different mounts. Borel's nickname is "Bo'rail'" due to his penchant for riding close to the rail to save ground.
Charles Bernard Borel was an American Thoroughbred horse racing jockey best known for winning the 1917 Kentucky Derby.
Diondre Michael Borel is an American football wide receiver who is currently a free agent. After playing college football for Utah State University, he was signed as an undrafted free agent by the Green Bay Packers in 2011. Borel was Utah State's starting quarterback from 2008 to 2010, finishing his collegiate career ranked second in school history with 6,698 passing yards and 8,096 yards total offense.
The Borel distribution is a discrete probability distribution, arising in contexts including branching processes and queueing theory. It is named after the French mathematician Émile Borel.
456 Montgomery Plaza is a 379 ft (116 m), 26-story class-A office skyscraper on Montgomery Street in the Financial District of San Francisco, California.
Nego do Borel, artistic name of Leno Maycon Viana Gomes, is a Brazilian singer of funk ostentação, songwriter and actor. He is known for hits "Os Cara do Momento", "Diamante de Lama", "Bonde dos Brabos" and "Você Partiu Meu Coração", with Wesley Safadão and Anitta. Currently he has two albums released by Sony Music. Nego do Borel was the sixth Brazilian artist to enter the US Billboard Hot 100.
Damien Borel is an American football defensive lineman who is currently a free agent. He attended Woodland High School and Butte College. In 2012, while at Butte, he tallied 69 tackles and 19 sacks. Borel's 19 sacks led all California Community College Athletic Association players in 2012.
"Você Partiu Meu Coração" is a song recorded by Brazilian Nego do Borel, featuring Brazilian singers Anitta and Wesley Safadão. It was written by Romeu R3, Jefferson Junior, and Umberto Tavarez, and was produced by Umberto Tavares and Mãozinha.
