Revolutionizing the calculus (1 resultados)

(Paris, Gauthier-Villars), 1901). 4to. No wrappers. In: "Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences", Tome 132, No 17. pp. (1013-) 1080. (Entire issue offered). Lebesgue's paper: pp. 1025-1028. Clean and fine. First printing of Lebesgue's seminal paper on the calculus, which generalized the Riemann integral."Building on the work of others, including that of Emile Borel and Camille Jordan, Lebesgue formulated the theory of measure in 1901 and in his famous paper Sur une generalisation de l'integrale definie, which appeared in the Comptes Rendus on 29 April 1901 (the paper offered), he gave the definition of the Lebesgue integral that generalises the notion of the Riemann integral by extending the concept of the area below a curve to include many discontinuous functions. This generalisation of the Riemann integral revolutionised the integral calculus. Up to the end of the 19th century, mathematical analysis was limited to continuous functions, based largely on the Riemann method of integration. There is a problem here, namely that a function which is not Riemann integrable may be represented as a uniformly bounded series of Riemann integrable functions. What made the new definition important was that Lebesgue was able to recognise in it an analytic tool capable of dealing with - and to a large extent overcoming - the numerous theoretical difficulties that had arisen in connection with Riemann's theory of integration.".…