Abstract
The integral of a real valued function over a set is a generalization of the notion of sum. It is defined by approximating in a suitable way by certain finite sums. The first careful definition was due to Riemann (1854). Riemann defined the integral of a function over an interval [a, b] of the real line E1. In the succeeding years Riemann’s idea was extended in several ways. However, the Riemann integral has several intrinsic drawbacks, and for a truly satisfactory treatment of integration a different approach had to be found.
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© 1977 Springer-Verlag, New York Inc.
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Fleming, W. (1977). Integration. In: Functions of Several Variables. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9461-7_5
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DOI: https://doi.org/10.1007/978-1-4684-9461-7_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9463-1
Online ISBN: 978-1-4684-9461-7
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