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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2406.02401 |
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| _version_ | 1866913779162284032 |
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| author | Hoareau, Fabien Maître, François Le |
| author_facet | Hoareau, Fabien Maître, François Le |
| contents | We show that up to a null set, every infinite measure-preserving action of a locally compact Polish group can be turned into a continuous measure-preserving action on a locally compact Polish space where the underlying measure is Radon. We also investigate the distinction between spatial and boolean actions in the infinite measure-preserving setup. In particular, we extend Kwiatkowska and Solecki's Point Realization Theorem to the infinite measure setup. We finally obtain a streamlined proof of a recent result of Avraham-Re'em and Roy: Lévy groups cannot admit nontrivial continuous measure-preserving actions on Polish spaces when the measure is locally finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02401 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spatial models for boolean actions in the infinite measure-preserving setup Hoareau, Fabien Maître, François Le Dynamical Systems Group Theory Operator Algebras We show that up to a null set, every infinite measure-preserving action of a locally compact Polish group can be turned into a continuous measure-preserving action on a locally compact Polish space where the underlying measure is Radon. We also investigate the distinction between spatial and boolean actions in the infinite measure-preserving setup. In particular, we extend Kwiatkowska and Solecki's Point Realization Theorem to the infinite measure setup. We finally obtain a streamlined proof of a recent result of Avraham-Re'em and Roy: Lévy groups cannot admit nontrivial continuous measure-preserving actions on Polish spaces when the measure is locally finite. |
| title | Spatial models for boolean actions in the infinite measure-preserving setup |
| topic | Dynamical Systems Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2406.02401 |