LEBESGUE, HENRI-LON

born June 28, 1875, Beauvais, Fr. died July 26, 1941, Paris French mathematician whose generalization of the Riemann integral revolutionized the field of integration. He was matre de confrences (lecture master) at the University of Rennes until 1906, when he went to Poitiers, first as charg de cours (assistant lecturer) of the faculty of sciences and later as professor. About six years later he went to Paris as matre de confrences, and afterward he became professor at the Collge de France. In 1917 he was awarded the Prix Saintour, and in 1922 he was elected to the Paris Academy of Sciences. He was made an honorary member of the London Mathematical Society in 1924 and a foreign member of the Royal Society of London in 1930. One of the greatest mathematicians of his day, Lebesgue's pavement theorem is an important contribution to topology, and he did some work on Fourier series and potential theory (the theory of functions describing a conservative energy field). However, his main work was in integration. Toward the close of the 19th century, mathematical analysis was limited effectually to continuous functions, and artificial restrictions were necessary to cope with discontinuities that cropped up with greater frequency as more exotic functions were encountered. The Riemann method of integration was applicable only to continuous and a few discontinuous functions. Influenced by the work of mile Borel, Camille Jordan, and others on theories of measure and content, Lebesgue formulated his theory of measure in 1901. In 1902 he framed a new definition of the definite integral. This Lebesgue integral is one of the great achievements of modern real analysis. With Lebesgue integration, any bounded, summable function is the derivative of its indefinite integral, except perhaps for an ensemble of points with zero measure. Lebesgue integration was also instrumental in greatly expanding the scope of Fourier analysis. In addition to about 50 papers, Lebesgue wrote two major books, Leons sur l'intgration et la recherche des fonctions primitives (1904; Lessons on Integration and Analysis of Primitive Functions) and Leons sur les sries trigonomtriques (1906; Lessons on the Trigonometric Series).