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Integration

  • J. L. Doob
Part of the Graduate Texts in Mathematics book series (GTM, volume 143)

Abstract

A positive step function f can be written uniquely in the form f = Σa1 A • a linear combination, with positive pairwise distinct coefficients, of indicator functions of a finite disjunct sequence of measurable sets. Define the integral of f on S with respect to λ, using this representation of f, by
$$ \int\limits_S {fd\lambda = \sum a \bullet \lambda \left( {A \bullet } \right)} . $$
(1.1)

Keywords

Measurable Function Measure Space Measure Theory Compact Interval Finite Measure 
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 Science+Business Media New York 1994

Authors and Affiliations

  • J. L. Doob
    • 1
  1. 1.UrbanaUSA

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