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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2410.18488 |
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| _version_ | 1866914092681265152 |
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| author | Meyerovitch, Tom Weiss, Benjamin |
| author_facet | Meyerovitch, Tom Weiss, Benjamin |
| contents | Kac's lemma determines the expected return time to a set of positive measure under iterations of an ergodic probability preserving transformations. We introduce the notion of an \emph{allocation} for a probability preserving action of a countable group. Using this notion, we formulate and prove generalization of Kac's lemma for an action of a general countable group, and another generalization that applies to probability preserving equivalence relations. As an application, we provide a short proof for the existence of countable generating partitions for any ergodic action of a countable group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18488 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kac's Lemma and countable generators for actions of countable groups Meyerovitch, Tom Weiss, Benjamin Dynamical Systems 37A15 Kac's lemma determines the expected return time to a set of positive measure under iterations of an ergodic probability preserving transformations. We introduce the notion of an \emph{allocation} for a probability preserving action of a countable group. Using this notion, we formulate and prove generalization of Kac's lemma for an action of a general countable group, and another generalization that applies to probability preserving equivalence relations. As an application, we provide a short proof for the existence of countable generating partitions for any ergodic action of a countable group. |
| title | Kac's Lemma and countable generators for actions of countable groups |
| topic | Dynamical Systems 37A15 |
| url | https://arxiv.org/abs/2410.18488 |