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Borel Sets, Random Variables, and Borel Functions

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Part of the Springer Texts in Statistics book series (STS)

Abstract

In Chapter 3, we note that the class of events is assumed to be a sigma algebra of subsets of the basic space Ω. In Appendix 2a, we characterize a sigma algebra of events as a class closed under complements and countable unions, and show that these conditions imply closure under countable intersections. Also, we introduce the notion of a sigma algebra generated by a class as the smallest sigma algebra that contains that class.

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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  1. 1.Department of Mathematical SciencesRice UniversityHoustonUSA

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