The integral from Riemann to Bourbaki

Henri Lebesgue

A chapter in Sets and integration An outline of the development, 1972, pp 75-154 from Springer

Abstract: Abstract Although I have the intention to write about the development of the integral in the period from Riemann into modern times, it would not be justified to pass over the two thousand years before Riemann in which several famous mathematicians studied this notion. By omitting entirely this long period, there would be no opportunity to mention the names of Euclides, Eudoxos, Archimedes, and, centuries later, Leibniz, Newton; without pretending that this list should be complete. This is all the more unjustified as there are several lines, leading from Antiquity to modern times. Therefore, a short introduction is necessary; I shall mention some ideas which return in our modern theories. In this introduction completeness is not aimed at.

Keywords: Bounded Variation; Descriptive Definition; Outer Measure; Primitive Function; Integral Calculus (search for similar items in EconPapers)
Date: 1972
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-010-2718-2_2

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DOI: 10.1007/978-94-010-2718-2_2

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