Finitely-additive, countably-additive and internal probability measures
| Autor: | Duanmu, Haosui, Weiss, William |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Commentationes Mathematicae Universitatis Carolinae, 2018 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 17 pages |
| Databáze: | arXiv |
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