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Lebesgue was born in Beauvais, France, and received his undergraduate college training in mathematics at the École Normale Supérieure in Paris. While teaching at the Lycée Centrale in Nancy, France, Lebesgue worked on his doctoral dissertation. In this work, he began to develop a new theory of integral calculus that grew from previous research by René Louis Baire (1875-1932) and Georg Riemann. Lebesgue finally received his doctorate in mathematics from the Sorbonne in 1902 and thereafter assumed various teaching positions before returning to the Sorbonne in 1910 as lecturer in mathematics. During this entire time, he absorbed the work of Camille Jordan (1838-1922) and Émile Borel (1871-1956) and continued his own work on integration theory. In 1901 he developed his new integral, which he made widely known through lectures at the Collège de France and through publication in the monograph series edit by Borel. Lebesgue's theory, which was fundamentally a generalization of Riemann's integral theory, included a measure-theoretic viewpoint that made the Lebesgue integral, as it became known, useful in several branches of mathematics, such as curve rectification and the theory of trigonometric series.
With success came promotions. In 1920 Lebesgue was appointed chair of his department at the Sorbonne, but he left the following year to take up his final post as professor of mathematics at the Collège de France. In 1922 Lebesgue's unique approach to integral theory was recognized with his election to the Académie des Sciences. By this time, he had produced about 90 books and papers, mostly on the subject of his own theory of integration. But Lebesgue contributed significant work in other areas of mathematics, as well, relating to the theory of sets and functions, the calculus of variations, the theory of surface area, and dimension theory.
During a period of seven years, Lebesgue received the Prix Houllevigue, the Prix Poncelet, the Prix Saintour, and the Prix Petit d'Ormoy--all for his contributions to mathematics. He remained active for the last two decades of his life, publishing papers that reflected his broadening interest in teaching. Lebesgue died in Paris in 1941.