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arXiv 2010.024632020-10-06math.LO

Finitely-additive, countably-additive and internal probability measures

Haosui Duanmu, William Weiss

备注：: 17 pages
发表信息：: Commentationes Mathematicae Universitatis Carolinae, 2018

英文摘要：

We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an internal probability measure and its push-down measure is infinitesimal. As an application to standard probability theory, we show that every finitely-additive Borel probability measure $P$ on a separable metric space is a limit of a sequence of countably-additive Borel probability measures if and only if the space is totally bounded.

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