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Lebesgue
Henri Léon Lebesgue (; ; June 28, 1875 – July 26, 1941) was a French mathematician known for his theory of integration, which was a generalization of the 17th-century concept of integration—summing the area between an axis and the curve of a function defined for that axis. His theory was published originally in his dissertation ''Intégrale, longueur, aire'' ("Integral, length, area") at the University of Nancy during 1902. Personal life Henri Lebesgue was born on 28 June 1875 in Beauvais, Oise. Lebesgue's father was a typesetter and his mother was a school teacher. His parents assembled at home a library that the young Henri was able to use. His father died of tuberculosis when Lebesgue was still very young and his mother had to support him by herself. As he showed a remarkable talent for mathematics in primary school, one of his instructors arranged for community support to continue his education at the Collège de Beauvais and then at Lycée Saint-Louis and Lycée Louis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lebesgue Measure
In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of higher dimensional Euclidean '-spaces. For lower dimensions or , it coincides with the standard measure of length, area, or volume. In general, it is also called '-dimensional volume, '-volume, hypervolume, or simply volume. It is used throughout real analysis, in particular to define Lebesgue integration. Sets that can be assigned a Lebesgue measure are called Lebesgue-measurable; the measure of the Lebesgue-measurable set A is here denoted by \lambda(A). Henri Lebesgue described this measure in the year 1901 which, a year after, was followed up by his description of the Lebesgue integral. Both were published as part of his dissertation in 1902. Definition For any interval I = ,b/math>, or I = (a, b), in the set \mathbb of real numbers, let \ell(I)= b - a denote its length. For any subset E\subseteq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lebesgue Integration
In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the axis. The Lebesgue integral, named after French mathematician Henri Lebesgue, is one way to make this concept rigorous and to extend it to more general functions. The Lebesgue integral is more general than the Riemann integral, which it largely replaced in mathematical analysis since the first half of the 20th century. It can accommodate functions with discontinuities arising in many applications that are pathological from the perspective of the Riemann integral. The Lebesgue integral also has generally better analytical properties. For instance, under mild conditions, it is possible to exchange limits and Lebesgue integration, while the conditions for doing this with a Riemann integral are comparatively baroque. Furthermore, the Lebesgue integral can be generalized in a straightforward way to more gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discontinuity (mathematics)
Continuous functions are of utmost importance in mathematics, functions and applications. However, not all Function (mathematics), functions are continuous. If a function is not continuous at a limit point (also called "accumulation point" or "cluster point") of its Domain of a function, domain, one says that it has a discontinuity there. The Set theory, set of all points of discontinuity of a function may be a discrete set, a dense set, or even the entire domain of the function. The Oscillation (mathematics), oscillation of a function at a point quantifies these discontinuities as follows: * in a removable discontinuity, the distance that the value of the function is off by is the oscillation; * in a jump discontinuity, the size of the jump is the oscillation (assuming that the value ''at'' the point lies between these limits of the two sides); * in an essential discontinuity (a.k.a. infinite discontinuity), oscillation measures the failure of a Limit of a function, limit to exist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georges De Rham
Georges de Rham (; 10 September 1903 – 9 October 1990) was a Swiss mathematician, known for his contributions to differential topology. Biography Georges de Rham was born on 10 September 1903 in Roche, a small village in the canton of Vaud in Switzerland. He was the fifth born of the six children in the family of Léon de Rham, a constructions engineer. Georges de Rham grew up in Roche but went to school in nearby Aigle, the main town of the district, travelling daily by train. By his own account, he was not an extraordinary student in school, where he mainly enjoyed painting and dreamed of becoming a painter. In 1919 he moved with his family to Lausanne in a rented apartment in Beaulieu Castle, where he would live for the rest of his life. Georges de Rham started the Gymnasium in Lausanne with a focus on humanities, following his passion for literature and philosophy but learning little mathematics. On graduating from the Gymnasium in 1921 however, he decided not to continu ... [...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] |
Zygmunt Janiszewski
Zygmunt Janiszewski (12 July 1888 – 3 January 1920) was a Polish mathematician. Early life and education He was born to mother Julia Szulc-Chojnicka and father, Czeslaw Janiszewski who was a graduate of the University of Warsaw and served as the director of the Société du Crédit Municipal in Warsaw. Janiszewski left Poland to study mathematics in Zürich, Munich and Göttingen, where he was taught by some of the most prominent mathematicians of the time, such as Heinrich Burkhardt, David Hilbert, Hermann Minkowski and Ernst Zermelo. He then went to Paris and in 1911 received his doctorate in topology under the supervision of Henri Lebesgue. His thesis was titled ''Sur les continus irréductibles entre deux points (On the Irreducible Continuous Curves Between Two Points)''. In 1913, he published a seminal work in the field of topology of surface entitled ''On Cutting the Plane by Continua''. Career Janiszewski taught at the University of Lwów and was professor at the Un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henri Lebègue
Henri Lebègue (27 February 1856 – 19 October 1938) was a French palaeographer, director of studies at the École pratique des hautes études. The French historian Ernest Lebègue (1862–1943), was his brother. Henri Lebègue was also the father of literary historian Raymond Lebègue and nephew of publisher and media owner Alphonse-Nicolas Lebègue (1814–1885) from Brussels. Palaeographer and professor at the École pratique des hautes études An officer of Public Instruction, attached to the library of the University of Paris ( Sorbonne) from November 1882 to October 1888, Henri Lebègue wa admitted to the École pratique des hautes études in November 1891 as head of palaeographic studies. He joined the section of historical and philological sciences. A researcher, Lebègue was also a translator and published texts by Greek authors related to the geography and history of Gaules. Henri Lebègue also wrote Greek exercise books. He listed and partly translated t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poncelet Prize
The Poncelet Prize () is awarded by the French Academy of Sciences. The prize was established in 1868 by the widow of General Jean-Victor Poncelet for the advancement of the sciences. It was in the amount of 2,000 francs (as of 1868), mostly for the work in applied mathematics. The precise wording of the announcement by the academy varied from year to year and required the work be "in mechanics", or "for work contributing to the progress of pure or applied mathematics", or simply "in applied mathematics", and sometimes included condition that the work must be "done during the ten years preceding the award." 19th century Source: * (1868) Alfred Clebsch * (1869) Julius von Mayer * (1870) Camille Jordan * (1871) Joseph Boussinesq * (1872) Amédée Mannheim, "for the general excellence of his geometrical disquisitions." * (1873) William Thomson, "for his magnificent works on the mathematical theory of electricity and magnetism." * (1874) Jacques Bresse, "for his work in applied m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lycée Saint-Louis
The Lycée Saint-Louis () is a selective post-secondary school located in the 6th arrondissement of Paris, 6th arrondissement of Paris, in the Latin Quarter. It is the only state-funded French lycée that exclusively offers ''Classe Préparatoire aux Grandes Écoles, classes préparatoires aux grandes écoles'' (''CPGE;'' preparatory classes for Grandes Écoles, French top-level educational institutions). Saint-Louis has graduated many notable alumni, including five Nobel Prize, Nobel laureates, one Fields Medal, Fields laureate, one Patrice de Mac Mahon, President of France, as well as major intellectual figures such as Antoine de Saint-Exupéry, Émile Zola or Louis Pasteur. History Collège d'Harcourt The Lycée Saint-Louis, formerly known as the ''Collège d'Harcourt'' (), was established in 1280 by Robert and Raoul d'Harcourt with the intention of providing food and lodging to approximately forty students from disadvantaged backgrounds. From its beginning, the institu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Poitiers
The University of Poitiers (UP; , ) is a public university located in Poitiers, France. It is a member of the Coimbra Group. It is multidisciplinary and contributes to making Poitiers the city with the highest student/inhabitant ratio in France by welcoming nearly 28,000 students in 2017. The University of Poitiers represents a global operating budget of around 150 million euros per year, one-third of which is for operating and investment costs and two-thirds for personnel costs. As of July 2015 it is a member of the regional university association Leonardo da Vinci consolidated University. History Founded in 1431 by Pope Eugene IV and chartered by King Charles VII of France, Charles VII, the University of Poitiers was originally composed of five faculties: theology, canon law, civil law, medicine, and arts. In the 16th century, the university exerted its influence over the town cultural life, and was ranked second only to Paris. Of the 4,000 students who attended it at the ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collège De France
The (), formerly known as the or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment () in France. It is located in Paris near La Sorbonne. The has been considered to be France's most prestigious research establishment. It is an associate member of PSL University. Research and teaching are closely linked at the , whose ambition is to teach "the knowledge that is being built up in all fields of literature, science and the arts". Overview As of 2021, 21 Nobel Prize winners and 9 Fields Medalists have been affiliated with the Collège. It does not grant degrees. Each professor is required to give lectures where attendance is free and open to anyone. Professors, about 50 in number, are chosen by the professors themselves, from a variety of disciplines, in both science and the humanities. The motto of the Collège is ''Docet Omnia'', Latin for "It teaches everything"; its goal is to "teach science in the making" and ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
