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Topic: Emile Felix Edouard Justin Borel

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	Borel, Emile Félix-Edouard-Justin (Site not responding. Last check: 2007-10-22)
		Borel was born in St-Affrique and studied in Paris.
		In the 1890s Borel did his most important work: on probability, the infinitesimal calculus, divergent series, and, most influential of all, the theory of measure.
		Borel's theory of integral functions and his analysis of measure theory and divergent series established him, alongside French mathematician Henri Lebesgue, as one of the founders of the theory of functions of real variables.
	www.cartage.org.lb /en/themes/biographies/mainbiographies/B/Borel/1.html (181 words)

	Encyclopaedia Britannica entry (Site not responding. Last check: 2007-10-22)
		This sensational accomplishment set the stage for his formulation of a theory of integral functions and the distribution of their values, a topic that dominated the theory of complex functions for the next 30 years.
		Although he was not the first to define a conventional sum of a divergent series (a series of numbers that does not approach a certain number), he was the first to conceive and develop a systematic theory of such series (1899).
		Borel also served in the French Chamber of Deputies (1924-36) and as minister of the navy (1925-40).
	www.aam314.vzz.net /EB/Borel.html (279 words)

	Borel (Site not responding. Last check: 2007-10-22)
		Emile Borel created the first effective theory of the measure of sets of points beginning of the modern theory of functions of a real variable.
		Borel was appointed to the École Normale Supérieure in Paris in 1896.
		Borel, although not the first to define the sum of a divergent series, was also the first to develop (1899) a systematic theory for a divergent series.
	www.math.uri.edu /~kulenm/mth381pr/GAMETH/Borel.html (260 words)

	Search Results for Borel
		Borel was an astute observer: he had an uncanny eye for artistic detail and would reflect on the influence of literature and culture on human outlook.
		Emile Borel was educated at the Ecole Normale Superieure in Paris.
		This result was strengthened by Borel in 1899 when he proved a lower bound for P(e), where P is a polynomial with integer coefficients, depending on the maximum modulus of the integer coefficients of P. Gelfond, Feldman's supervisor, had extended Borel's result to numbers of the form alpha beta, where alpha, beta are algebraic numbers.
	www-history.mcs.st-and.ac.uk /Search/historysearch.cgi?SUGGESTION=Borel&CONTEXT=1 (3064 words)

	Wikipedia:Today's featured article/October 31, 2004 - Wikipedia, the free encyclopedia
		The "infinite monkey theorem" is a popular misnomer for an idea from Émile Borel's book on probability, published in 1909.
		The book introduced the concept of "dactylographic monkeys" seated in front of typewriter keyboards and hitting keys at random.
		Borel exemplified a proposition in the theory of probability called Kolmogorov's zero-one law by saying that the probability is one that such a monkey will eventually type every book in France's Bibliothèque nationale (national library).
	en.wikipedia.org /wiki/Wikipedia:Today's_featured_article/October_31,_2004 (191 words)

	Félix Edouard Justin Emile Borel Biography / Biography of Félix Edouard Justin Emile Borel 1900 To 1949: ...
		Borel was born the son of Honoré, a pastor, and Emilie Teissié-Solier Borel, in the French town of Saint-Affrique on January 7, 1871.
		Borel went on to the Ecole Normale Supériere, a preeminent school in science and mathematics with which he would remain connected for most of his life.
		Borel in 1899 became the first mathematician to develop a systematic theory for a divergent series.
	www.bookrags.com /biography-flix-edouard-justin-emile-borel-scit-06123 (720 words)

	Borel biography
		Borel created the first effective theory of the measure of sets of points.
		Borel, although not the first to define the sum of a divergent series, was the first to develop a systematic theory for a divergent series which he did in 1899.
		After 1924, Borel became active in the French government serving in the French Chamber of Deputies (1924-36) and as Minister of the Navy (1925-40).
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Borel.html (477 words)

	Academic Genealogy
		Felix Edouard Justin Emile Borel was academic and statesman.
		Borel was awarded the Croix de Guerre in 1918, the Resistance Medal in 1945, and the Grand Croix Legion d'Honneur in 1950.
		In probability theory, Borel's name, along with Francesso Cantelli, is linked to the famous Borel-Cantelli lemmas that give conditions for the occurrence of infinitely many events to have probability 0 or 1.
	www.cs.ualberta.ca /~zaiane/htmldocs/acgenealogy.html (488 words)

	Felix Edouard Justin Emile Borel Biography
		Felix Edouard Justin Emile Borel (January 7, 1871 - February 3, 1956) was a French mathematician and politician.
		The concept of a Borel set is named in his honor.
		One of his books on probability introduced the amusing thought experiment that entered popular culture under the name infinite monkey theorem or the like.
	www.biographybase.com /biography/Borel_Felix_Edouard_Justin_Emile.html (156 words)

	MATHEMATIC DICTIONARY
		BOREL first definition of the sum of a di-vergent series.
		Borel's integral definition of the sum of a divergent series.
		Any set which can be obtained from lhe closed and open sets on the real line by repeated applications of operations of union and intersection to denumerable numÂ bers of sets.
	mathdict.com /6.html (2994 words)

	Ars Libri, Ltd.
		"One of the features of Manet's portrait of Emile Zola painted for the Salon of 1868 [Paris, Musée d'Orsay] is a superb still life composed of books, pamphlets, the writer's quill pen and inkpot, and his pipe, scattered over his work table.
		Catalogue raisonné of his prints by Michael Justin Wentworth.
		Directed and coordinated by Charles S. Moffett with the assistance of Ruth Berson and Barbara Lee Williams, Fronia E. Wissman.
	www.arslibri.com /mfa001_monet.htm (2585 words)

	A Minimalist Program for Linguistics
		Even mathematics depends upon the "background vernacular" of language, as noted by Borel (1928:160), quoted in Ryckman (1986:289-90).
		And as Borel observes, the crucial role of language in all this is usually unnoticed.
		As did Bloomfield, for instance, where he stated (1927:142) "In the study of linguistic forms, therefore, I should not appeal, as Jespersen sometimes does, to meaning as if it were separable from form", or further:
	www.dmi.columbia.edu /zellig/Minimalist.html (14091 words)

	January 7 - Today in Science History (Site not responding. Last check: 2007-10-22)
		Born 7 Jan 1871; died 3 Feb 1956.
		(Félix-Édouard-Justin-) Émile Borel was a French mathematician who (with René Baire and Henri Lebesgue), was among the pioneers of measure theory and its application to probability theory.
		In one of his books on probability, he proposed the thought experiment that a monkey hitting keys at random on a typewriter keyboard will - with absolute certainty - eventually type every book in France's Bibliothèque nationale de France (National Library).
	www.todayinsci.com /1/1_07.htm (2289 words)

	ContractsProf Blog: January 3, 2005 - January 9, 2005
		While surveying the route of the transcontinental Canadian Pacific Railway, he will come up with the idea of standard time zones as a way to simplify scheduling and control.
		1871: Félix-Édouard-Justin-Émile Borel is born in St. Affrique, France.
		He is best known as the inventor of the “infinite monkey theorem,” under which a monkey given an infinite amount of time will inevitably type out every manuscript in the Bibliothèque Nationale de France.
	lawprofessors.typepad.com /contractsprof_blog/2005/week1 (5658 words)

	PSIgate - Physical Sciences Information Gateway: Search/Browse Results
		Paul Emile Appell Born: 27 Sept 1855 in Strasbourg, France Died: 24 Oct 1930 Click the picture above to see four larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main...
		Felix Christian Klein Born: 25 April 1849 in Düsseldorf, Prussia (now Germany) Died: 22 June 1925 in Göttingen, Germany Click the picture above to see seven larger pictures Show birthplace location Previous (Chronologically) Next Biographies I...
		Félix Edouard Justin Emile Borel Born: 7 Jan 1871 in Saint Affrique, Aveyron, Midi-Pyrénées, France Died: 3 Feb 1956 in Paris, France Click the picture above to see four larger pictures Show birthplace location Previous (Chronologically) Next...
	www.psigate.ac.uk /roads/cgi-bin/search_webcatalogue2.pl?limit=1525&term1=pictures (934 words)

	Foreword, Vol. 1: Philosophy of science, syntax, and semantics (Site not responding. Last check: 2007-10-22)
		Symbolic and mathematical representations depend upon language for their definitions and function as convenient graphical abbreviations that in any science are in practice routinely read out as sentences in oral presentations.
		Even mathematics depends upon the ‘background vernacular’ of language, although, as Borel
		To be sure, the study of phonetics is systematized in a theoretical framework, and in the interaction of speech physiology and acoustics there can be preferential ‘affordances’ for effecting the contrasts of languages (to borrow Gibson’s term without buying with it his psychology), as in ‘quantal’ aspects of speech.
	www.dmi.columbia.edu /zellig/Foreword1.html (9049 words)

	USATODAY.com (Site not responding. Last check: 2007-10-22)
		Categorized by state, these miniature works of art offer a rich look at a nation ever in the process of re-inventing itself.
		American Pi How can you lose with a trivia game whose multiple choice selections include 'Félix-Édouard-Justin Émile Borel,' '3arctan 1/256 + 2arctan 1/17' and 'exploding pop-tarts?' Test your mathematical knowledge playing the best kept secret in party games: Pi Trivia.
		Click on the image for Hot Site details.
	www.usatoday.com /tech/2002/06/27/hotsites.htm (251 words)

	Bibliography (Site not responding. Last check: 2007-10-22)
		Henri de Senarmont, Emile Verdet et Leonor Fresne
		Oeuvres / publiees sous les auspices de l'Academie des Sciences, par Emile Picard
		Korrespondenz Felix Klein--Adolph Mayer : Auswahl aus den Jahren 1871-1907
	www.library.cornell.edu /math/bibliography/display.cgi (6229 words)

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