Abstract
We want to extend the concept of convergence in distribution to probability spaces other than (ℝ, 𝛣). Certain metric spaces, known as ‘Polish spaces’, play a central role. Particularly important examples of Polish spaces are the real line, the extended real line, d-dimensional Euclidean space, infinite products of intervals, and spaces of continuous functions. Thus, this chapter may be viewed as a mechanism for extending the concepts and results discussed in Chapter 14 to a wide variety of settings. (Basic facts about metric spaces are treated briefly in Appendix B. Some of the topology in Appendix C is also relevant.)KeywordsPolish SpaceConvergent SubsequenceProduct TopologyCountable ProductPreceding PropositionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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