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

Convolution 

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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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