Borel Sets, Random Variables, and Borel Functions
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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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