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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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VI.72 Henri Lebesgue

b. Beauvais, France, 1875; d. Paris, 1941Theory of the integral; measure; applications in Fourier analysis;dimension in topology; calculus of variations

Lebesgue studied at the École Normale in Paris (1894-97), where he was influenced by the slightly older BOREL [VI.70] and René-Louis Baire. As a teacher at Nancy he completed his seminal thesis “Intégrale, longueure, aire” (1902). After university positions in Rennes, Poitiers, and at the Sorbonne in Paris, and following war-related research, Lebesgue became a professor at the Sorbonne (1919) and then, finally, at the Collège de France (1921). One year later he was elected to the French Academy of Sciences.

Lebesgue’s most important achievement was his generalization of ...

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