Abstract
Soon after Riemann’s definition of the integral in 1854, its limitations became apparent. Numerous definitions of the integral for bounded as well as unbounded functions were successively proposed after 1854. At the beginning of this century, the French mathematician Henri Lebesgue (1875–1941) introduced in his doctoral dissertation at the Sorbonne, “Intégral, longueur, aire” (1902), a notion of the integral that was to become the keystone of modern analysis.
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© 1995 Springer Science+Business Media New York
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Chae, S.B. (1995). The Lebesgue Integral: Riesz Method. In: Lebesgue Integration. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0781-8_3
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DOI: https://doi.org/10.1007/978-1-4612-0781-8_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94357-2
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