Borel Sets, Random Variables, and Borel Functions

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


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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