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.
KeywordsMonotone Sequence Nondecreasing Sequence Normed Vector Space Iterate Integral Regular Transformation
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