Finitely additive, Countably additive and Internal Probability Measures


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.

Commentationes Mathematicae Universitatis Carolinae, vol. 59 (2018), issue 4, pp. 467–485