Integration in a Probability Space

  • Yuan Shih Chow
  • Henry Teicher
Part of the Springer Texts in Statistics book series (STS)


There are two basic avenues to integration. In the modern approach the integral is introduced first for simple functions—as a weighted average of the values of the function—and then defined for any nonnegative measurable Function f as a limit of the integrals of simple nonnegative functions increasing to f. Conceptually this is extremely simple, but a certain price is paid in terms of proofs. The alternative classical approach, while employing a less intuitive definition, achieves considerable simplicity in proofs of elementary properties.


Random Walk Probability Space Simple Random Walk Monotone Convergence Theorem Markov Inequality 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Yuan Shih Chow
    • 1
  • Henry Teicher
    • 2
  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of StatisticsRutgers UniversityNew BrunswickUSA

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