Stone-Cech extensions of probability measure spaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915066009354240 |
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| author | Reznichenko, E. A. |
| author_facet | Reznichenko, E. A. |
| contents | It is proved that $P(βX)=βP(X)$ if and only if $P(X)$ is a pseudocompact space, where $P(X)$ is the space of probability Radon measures with weak topology and $βX$ is a Stone-Cech extension of the space $X$. A locally compact pseudocompact space $X$ is constructed such that $P(X)$ is not pseudocompact. Conditions are obtained under which $P(X)$ is pseudocompact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11838 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stone-Cech extensions of probability measure spaces Reznichenko, E. A. General Topology Functional Analysis Probability It is proved that $P(βX)=βP(X)$ if and only if $P(X)$ is a pseudocompact space, where $P(X)$ is the space of probability Radon measures with weak topology and $βX$ is a Stone-Cech extension of the space $X$. A locally compact pseudocompact space $X$ is constructed such that $P(X)$ is not pseudocompact. Conditions are obtained under which $P(X)$ is pseudocompact. |
| title | Stone-Cech extensions of probability measure spaces |
| topic | General Topology Functional Analysis Probability |
| url | https://arxiv.org/abs/2412.11838 |