| Title:
|
Finitely-additive, countably-additive and internal probability measures (English) |
| Author:
|
Duanmu, Haosui |
| Author:
|
Weiss, William |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
467-485 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\{P_n\}_{n\in \mathbb{N}}$ in the sense that $\int f \,{\rm d} P=\lim_{n\to \infty} \int f\, {\rm d} P_n$ for all bounded uniformly continuous real-valued function $f$ if and only if the space is totally bounded. (English) |
| Keyword:
|
nonstandard model in mathematics |
| Keyword:
|
nonstandard analysis |
| Keyword:
|
nonstandard measure theory |
| Keyword:
|
convergence of probability measures |
| MSC:
|
03H05 |
| MSC:
|
26E35 |
| MSC:
|
28E05 |
| MSC:
|
60B10 |
| idZBL:
|
Zbl 06997363 |
| idMR:
|
MR3914713 |
| DOI:
|
10.14712/1213-7243.2015.270 |
| . |
| Date available:
|
2018-12-28T15:10:25Z |
| Last updated:
|
2021-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147551 |
| . |
| Reference:
|
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| . |
