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Borel
Borel may refer to: People * Antoine Borel (1840–1915), a Swiss-born American businessman * Armand Borel (1923–2003), a Swiss mathematician * Borel (author), 18th-century French playwright * Borel (1906–1967), pseudonym of the French actor Jacques Henri Cottance * Émile Borel (1871–1956), a French mathematician known for his founding work in the areas of measure theory and probability * Mary Grace Borel (1915–1998), American socialite * Pascal Borel (born 1978), German footballer * Pierre Borel, 17th-century French chemist Places * Borel (crater), a lunar crater, named after Émile Borel Mathematics * Borel algebra, operating on Borel sets, named after Émile Borel, also: ** Borel measure, the measure on a Borel algebra * Borel distribution, a discrete probability distribution, also named after Émile Borel * Borel subgroup In the theory of algebraic groups, a Borel subgroup of an algebraic group ''G'' is a maximal Zariski closed and connected solvable algebraic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antoine Borel
Antoine Borel (December 29, 1840 – March 26, 1915) was a Swiss-American banker who ran the eponymous Borel & Co., headquartered in San Francisco, California. He was born in Neuchâtel, Switzerland and emigrated to the United States in 1862, where he joined his brother's bank and served as a Swiss Consul (representative), consul and director for several companies, including the Spring Valley Water Company, the California Street Cable Railroad, California Street Cable Company, and the Bankers' Investment Company. He died following an operation in Switzerland, to where he had returned in July 1914 for health issues. Early life Borel was born in Neuchâtel, Switzerland, to a wealthy merchant family, and completed his education in Switzerland and Germany. He emigrated to San Francisco, arriving in 1862, following his brother Alfred, who had arrived in 1855. Career Alfred Borel founded Borel & Co. in 1852; Antoine joined him in 1862, and the business was turned over to Antoine whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borel Algebra
In mathematics, a Borel set is any subset of a topological space that can be formed from its open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are named after Émile Borel. For a topological space ''X'', the collection of all Borel sets on ''X'' forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on ''X'' is the smallest σ-algebra containing all open sets (or, equivalently, all closed sets). Borel sets are important in measure theory, since any measure defined on the open sets of a space, or on the closed sets of a space, must also be defined on all Borel sets of that space. Any measure defined on the Borel sets is called a Borel measure. Borel sets and the associated Borel hierarchy also play a fundamental role in descriptive set theory. In some contexts, Borel sets are defined to be generated by the compact sets of the topological ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Armand Borel
Armand Borel (21 May 1923 – 11 August 2003) 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. Biography He studied at the ETH Zürich, where he came under the influence of the topologist Heinz Hopf and Lie-group theorist Eduard Stiefel. He was in Paris from 1949: he applied the Leray spectral sequence to the topology of Lie groups and their classifying spaces, under the influence of Jean Leray and Henri Cartan. With Hirzebruch, he significantly developed the theory of characteristic classes in the early 1950s. He collaborated with Jacques Tits in fundamental work on algebraic groups, and with Harish-Chandra on their arithmetic subgroups. In an algebraic group ''G'' a '' Borel subgroup'' ''H'' is one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Émile Borel
Félix Édouard Justin Émile Borel (; 7 January 1871 – 3 February 1956) was a French people, French mathematician and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability. Biography Borel was born in Saint-Affrique, Aveyron, the son of a Protestant pastor. He studied at the Collège Sainte-Barbe and Lycée Louis-le-Grand before applying to both the École normale supérieure (Paris), École normale supérieure and the École Polytechnique. He qualified in the first position for both and chose to attend the former institution in 1889. That year he also won the concours général, an annual national mathematics competition. After graduating in 1892, he placed first in the agrégation, a competitive civil service examination leading to the position of professeur agrégé. His thesis, published in 1893, was titled ''Sur quelques points de la théorie des fonctions'' ("On some points in the theory of functions"). That y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borel Measure
In mathematics, specifically in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets (and thus on all Borel sets). Some authors require additional restrictions on the measure, as described below. Formal definition Let X be a locally compact Hausdorff space, and let \mathfrak(X) be the smallest σ-algebra that contains the open sets of X; this is known as the σ-algebra of Borel sets. A Borel measure is any measure \mu defined on the σ-algebra of Borel sets. A few authors require in addition that \mu is locally finite, meaning that every point has an open neighborhood with finite measure. For Hausdorff spaces, this implies that \mu(C) 0 and ''μ''(''B''(''x'', ''r'')) ≤ ''rs'' holds for some constant ''s'' > 0 and for every ball ''B''(''x'', ''r'') in ''X'', then the Hausdorff dimension dimHaus(''X'') ≥ ''s''. A partial converse is provided by the Frostman lemma: Lemma: Let ''A'' be a Borel subset of R''n'', and let ''s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mary Grace Borel
Mary Grace Borel Shumate Marshal Sweet Paxton (October 31, 1915May 18, 1998) was an American socialite and film actress. She was the granddaughter of Antoine Borel, a San Francisco banker and consul general of Switzerland, and her family was prominent on the San Francisco social scene. Her debut was attended by 200 guests in 1934. Her 1935 marriage to the physician son of the San Francisco Police Commissioner was said to be "the highlight of the 1935 social season". Two years later she sued for divorce and, in 1938, remarried to film actor Alan Marshal, with whom she had one son. She sued for divorce in 1947; she later remarried two more times. Using the stage name Mary Marshall, she acted in two films and two television series. Upon her death in 1998, she was buried in the same crypt as her second husband, Alan Marshal. Early life and education Mary Grace Borel was born in San Francisco, California, on October 31, 1915. She was the eldest daughter of Antoine A. Borel, Jr., and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borel (surname)
Borel is a surname. Notable people with the surname include: * Adrien Borel (1886–1966), psychiatrist and psychoanalyst * Aldo Borel (1912–1979), Italian football player * André Borel d'Hauterive (1812–1896), French historian *Armand Borel (1923–2003), Swiss mathematician * Calvin Borel, American jockey *Cleopatra Borel (born 1979), Trinidadian athlete * Daniel Borel (born 1950), Swiss engineer *Émile Borel (1871–1956), French mathematician and politician *Éric Borel (1978–1995), French serial killer * Ernesto Borel (1889–1951), Italian footballer * Eugène Borel (1835–1892), Swiss politician * Felice Borel (1914–1993), Italian footballer * Frédéric Borel (born 1959), French architect * Gabriel Borel, French aircraft designer *George Frederik Willem Borel, Dutch military figure * Henri Borel, Dutch writer, son of George Frederik Willem Borel * Jacques Borel, French novelist * Jean-Louis Borel (1809–1884), French general * Marguerite Borel (1883–1969), Fren ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borel Distribution
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. If the number of offspring that an organism has is Poisson-distributed, and if the average number of offspring of each organism is no bigger than 1, then the descendants of each individual will ultimately become extinct. The number of descendants that an individual ultimately has in that situation is a random variable distributed according to a Borel distribution. Definition A discrete random variable ''X'' is said to have a Borel distribution with parameter ''μ'' ∈ ,1if the probability mass function of ''X'' is given by :P_\mu(n)= \Pr(X=n)= \frac for ''n'' = 1, 2, 3 .... Derivation and branching process interpretation If a Galton–Watson branching process has common offspring distribution Poisson with mean ''μ'', then the total number of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borel Subgroup
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 general linear group ''GLn'' (''n x n'' invertible matrices), the subgroup of invertible upper triangular matrices is a Borel subgroup. For groups realized over algebraically closed fields, there is a single conjugacy class of Borel subgroups. Borel subgroups are one of the two key ingredients in understanding the structure of simple (more generally, reductive) algebraic groups, in Jacques Tits' theory of groups with a (''B'', ''N'') pair. Here the group ''B'' is a Borel subgroup and ''N'' is the normalizer of a maximal torus contained in ''B''. The notion was introduced by Armand Borel, who played a leading role in the development of the theory of algebraic groups. Parabolic subgroups Subgroups between a Borel subgroup ''B'' and the ambient group ''G'' are called parabolic subgroups. Parabolic subgr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pascal Borel
Pascal Borel (born 26 September 1978) is a German football coach and former player who played as a goalkeeper. In 1999, Borel earned two caps for Germany at the U21 level. Playing career Borel was born in Karlsruhe. He played for FC Germania Friedrichstal and Waldhof Mannheim before joining Werder Bremen in 1998 where he stayed until 2005. During his time at Werder Bremen he and goalkeeping rival Jakub Wierzchowski were labelled the "weakest goalkeepers in the Bundesliga" by Süddeutsche Zeitung journalist Ralf Wiegand. In season 2007–08, he was part of Budapest Honvéd, where he made eight appearances playing in the Hungarian League. In March 2009, Borel signed with Chernomorets Burgas until the end of the season. On 4 April 2009, he made his competitive debut for the team in a match against Lokomotiv Sofia. Borel quickly became part of the main team and on 28 May 2009 he received a new contract with the club until the end of 2010–11 season. He left the club on 10 Ju ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Borel
Pierre Borel (; – 1671) was a French chemist, alchemist, physician, and botanist. Biography Borel was born in Castres . He became a doctor of medicine at the University of Montpellier in 1640. In 1654, he became physician to the King of France, Louis XIV. In 1663, he married Esther de Bonnafous. In 1674, he became a member of the Académie française. He died in Paris in 1671. He concerned himself with an eclectic range of subjects such as optics, ancient history, philology, and bibliography. Borel appears in the novel '' The Case of Charles Dexter Ward'' by H. P. Lovecraft Howard Phillips Lovecraft (, ; August 20, 1890 – March 15, 1937) was an American writer of Weird fiction, weird, Science fiction, science, fantasy, and horror fiction. He is best known for his creation of the Cthulhu Mythos. Born in Provi ..., where he is represented as a necromancer. The novel begins with a quote from him. Works * ''Les antiquités de Castres'', 1649 * ''Bibliotheca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borel (author)
Borel (18th-century, Rouen – ? ) was an 18th-century French playwright from Normandy. Already made known by some poetic essays and an epigram An epigram is a brief, interesting, memorable, sometimes surprising or satirical statement. The word derives from the Greek (, "inscription", from [], "to write on, to inscribe"). This literary device has been practiced for over two millennia ... in Latin entitled ''Nicetas'', crowned by the Palinod, Académie des Palinods in 1749, Borel Borel addressed the dramatic genre with a play, ''le Méfiant'' ("The distrustful"), comedy in five acts and in verse, premiered in Paris at the Comédie Italienne, 20 December 1785, where it was well received. Despite this happy first attempt in literary career, the silence of the biographies on Borel from that time suggests he stopped there. Works *1786: ''Le Méfiant, comédie en 5 actes et en vers'', Paris, Cailleau. Sources * Théodore-Éloi Lebreton''Biographie rouennaise'' Rouen, Le Br ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
