19 Facts About Henri Lebesgue

Henri Lebesgue's theory was published originally in his dissertation Integrale, longueur, aire at the University of Nancy during 1902.

Henri Lebesgue was born on 28 June 1875 in Beauvais, Oise.

Henri Lebesgue's parents assembled at home a library that the young Henri was able to use.

Henri Lebesgue's father died of tuberculosis when Lebesgue was still very young and his mother had to support him by herself.

In 1894, Henri Lebesgue was accepted at the Ecole Normale Superieure, where he continued to focus his energy on the study of mathematics, graduating in 1897.

Henri Lebesgue married the sister of one of his fellow students, and he and his wife had two children, Suzanne and Jacques.

In 1910 Henri Lebesgue moved to the Sorbonne as a maitre de conferences, being promoted to professor starting in 1919.

Between March 1899 and April 1901 Henri Lebesgue published six notes in Comptes Rendus.

The first of these, unrelated to his development of Henri Lebesgue integration, dealt with the extension of Baire's theorem to functions of two variables.

Henri Lebesgue turned next to trigonometric functions with his 1903 paper "Sur les series trigonometriques".

Henri Lebesgue presented three major theorems in this work: that a trigonometrical series representing a bounded function is a Fourier series, that the n Fourier coefficient tends to zero, and that a Fourier series is integrable term by term.

Henri Lebesgue expounds on Fourier series, Cantor-Riemann theory, the Poisson integral and the Dirichlet problem.

Henri Lebesgue had a disagreement with Emile Borel about whose integral was more general.

Henri Lebesgue invented a new method of integration to solve this problem.

Henri Lebesgue's idea was to first define measure, for both sets and functions on those sets.

Henri Lebesgue then proceeded to build the integral for what he called simple functions; measurable functions that take only finitely many values.

Henri Lebesgue integration has the property that every function defined over a bounded interval with a Riemann integral has a Henri Lebesgue integral, and for those functions the two integrals agree.

However, the Henstock integral depends on specific ordering features of the real line and so does not generalise to allow integration in more general spaces, while the Henri Lebesgue integral extends to such spaces quite naturally.

In 1947 Norbert Wiener claimed that the Henri Lebesgue integral had unexpected but important implications in establishing the validity of Willard Gibbs' work on the foundations of statistical mechanics.