Finitely additive, Countably additive and Internal Probability Measures

Abstract

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 on a separable metric space is a limit of a sequence of countably-additive Borel probability measures.

Publication
To appear in the Commentationes Mathematicae Universitatis Carolinae
Date
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