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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 ''n''-dimensional Euclidean space. For ''n'' = 1, 2, or 3, it coincides with the standard measure of length, area, or volume. In general, it is also called ''n''-dimensional volume, ''n''-volume, 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 ''λ''(''A''). Henri Lebesgue described this measure in the year 1901, followed the next year 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\mathbb, the Lebesgue oute ... [...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, extends the integral to a larger class of functions. It also extends the domains on which these functions can be defined. Long before the 20th century, mathematicians already understood that for non-negative functions with a smooth enough graph—such as continuous functions on closed bounded intervals—the ''area under the curve'' could be defined as the integral, and computed using approximation techniques on the region by polygons. However, as the need to consider more irregular functions arose—e.g., as a result of the limiting processes of mathematical analysis and the mathematical theory of probability—it became clear that more careful approximation techniques were needed to define a suitable integral. Also, one might ... [...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 function, continuous. If a function is not continuous at a point in 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. This article describes the classification of discontinuities in the simplest case of functions of a single Real number, real Variable-sweep wing, variable taking real values. 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); * i ... [...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 continue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Émile Borel
Félix Édouard Justin Émile Borel (; 7 January 1871 – 3 February 1956) was a French mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ... 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 agrégati ... [...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 Zurich, 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 Uni ... [...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 (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 palaeography, 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 liste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poncelet Prize
The Poncelet Prize (french: Prix Poncelet) 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 * (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 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lycée Saint-Louis
The lycée Saint-Louis is a highly selective post-secondary school located in the 6th arrondissement of Paris, in the Latin Quarter. It is the only public French lycée exclusively dedicated to providing ''classes préparatoires aux grandes écoles'' (''CPGE;'' preparatory classes for the Grandes Écoles such as École Polytechnique, CentraleSupélec in engineering and ESSEC Business School, ESCP Business School, and HEC Paris in commerce). It is known for the quality of its teaching, low acceptance rate and the results it achieves in their intensely competitive entrance examinations (''concours''). It is widely regarded as one of the best preparatory class in France and one of the most elitist and prestigious along with its neighbours from the Sainte-Geneviève hill the lycée Henri IV and the lycée Louis-Le-Grand. Saint-Louis has graduated many notable alumni, including five Nobel laureates, one Fields laureate, one President of France, as well as major intellectual figures ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collège De France
The Collège de France (), formerly known as the ''Collège Royal'' or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment (''grand établissement'') in France. It is located in Paris near La Sorbonne. The Collège de France is considered to be France's most prestigious research establishment. Research and teaching are closely linked at the Collège de France, whose ambition is to teach "the knowledge that is being built up in all fields of literature, science and the arts". It offers high-level courses that are free, non-degree-granting and open to all without condition or registration. This gives it a special place in the French intellectual landscape. Overview The Collège is considered to be France's most prestigious research establishment. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beauvais
Beauvais ( , ; pcd, Bieuvais) is a city and commune in northern France, and prefecture of the Oise département, in the Hauts-de-France region, north of Paris. The commune of Beauvais had a population of 56,020 , making it the most populous city in the Oise department, and third most-populous in Picardy. Together with its suburbs and satellite towns, the metropolitan area of Beauvais has a population of 128,020. The region around Beauvais is called the Beauvaisis. History Beauvais was known to the Romans by the Gallo-Roman name of ''Caesaromagus'' (''magos'' is Common Celtic for "field"). The post-Renaissance Latin rendering is ''Bellovacum'' from the Belgic tribe the Bellovaci, whose capital it was. In the ninth century it became a county (comté), which about 1013 passed to the bishops of Beauvais, who became peers of France from the twelfth century. This cites V. Lhuillier, ''Choses du vieux Beauvais et du Beauvaisis'' (1896). At the coronations of kings the Bishop of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lycée Louis-le-Grand
The Lycée Louis-le-Grand (), also referred to simply as Louis-le-Grand or by its acronym LLG, is a public Lycée (French secondary school, also known as sixth form college) located on rue Saint-Jacques in central Paris. It was founded in the early 1560s by the Jesuits as the ''Collège de Clermont'', was renamed in 1682 after King Louis XIV ("Louis the Great"), and has remained at the apex of France's secondary education system despite its disruption in 1762 following the suppression of the Society of Jesus. It offers both a high school curriculum, and a Classes Préparatoires post-secondary-level curriculum in the sciences, business and humanities. The strict admission process is based on academic grades, drawing from middle schools (for entry into high school) and high schools (for entry into the preparatory classes) throughout France. Its educational standards are highly rated and the working conditions are considered optimal due to its demanding recruitment of teachers. L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
