Automorphism groups of measures on the Cantor space. Part I: Good measures and Rokhlin properties
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910802637750272 |
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| author | Doucha, Michal Kwietniak, Dominik Malicki, Maciej Niemiec, Piotr |
| author_facet | Doucha, Michal Kwietniak, Dominik Malicki, Maciej Niemiec, Piotr |
| contents | We study criteria for the existence of a dense or comeager conjugacy class in the automorphism group of a given measure on the Cantor space. We concentrate on good measures, defined by Akin [\emph{Trans.\ Amer.\ Math.\ Soc.} \textbf{357} (2005), no. 7, 2681--2722], which we characterize as a particular subclass of ultrahomogeneous measures. We determine good measures with rational values on clopen sets whose automorphism group admits a comeager conjugacy class. Our approach uses the Fraïssé theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_17098 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Automorphism groups of measures on the Cantor space. Part I: Good measures and Rokhlin properties Doucha, Michal Kwietniak, Dominik Malicki, Maciej Niemiec, Piotr Logic Dynamical Systems We study criteria for the existence of a dense or comeager conjugacy class in the automorphism group of a given measure on the Cantor space. We concentrate on good measures, defined by Akin [\emph{Trans.\ Amer.\ Math.\ Soc.} \textbf{357} (2005), no. 7, 2681--2722], which we characterize as a particular subclass of ultrahomogeneous measures. We determine good measures with rational values on clopen sets whose automorphism group admits a comeager conjugacy class. Our approach uses the Fraïssé theory. |
| title | Automorphism groups of measures on the Cantor space. Part I: Good measures and Rokhlin properties |
| topic | Logic Dynamical Systems |
| url | https://arxiv.org/abs/2501.17098 |