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Integration

  • Wendell Fleming
Part of the Undergraduate Texts in Mathematics book series (UTM)

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.

Keywords

Monotone Sequence Nondecreasing Sequence Normed Vector Space Iterate Integral Regular Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • Wendell Fleming
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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