Leçons sur les Séries Trigonométriques Proféssees au College de France

The two great works of the celebrated French mathematician Henri Lebesgue (1875–1941), Leçons sur l'intégration et la recherche des fonctions primitives professées au Collège de France (1904) and Leçons sur les séries trigonométriques professées au Collège de France (1906) arose from lecture courses he gave at the Collège de France while holding a teaching post at the University of Rennes. In 1901 Lebesgue formulated measure theory; and in 1902 his new definition of the definite integral, which generalised the Riemann integral, revolutionised integral calculus and greatly expanded the scope of Fourier analysis. The Lebesgue integral is regarded as one of the major achievements in modern real analysis, and remains central to the study of mathematics today. Both of Lebesgue's books are reissued in this series.

Préface; Introduction; 1. Détermination des coefficients des séries trigonométriques représentant une fonction donnée; 2. Théorie élémentaire des séries de Fourier; 3. Séries de Fourier convergentes; 4. Séries de Fourier quelconques; 5. Séries trigonométriques quelconques; Table des matières.

The new definition by Henri Lebesgue (1875-1941) of the definite integral revolutionised integral calculus and the scope of Fourier analysis. The Lebesgue integral is regarded as one of the major achievements in modern real analysis, and remains central to the study of mathematics today.