On a theorem Dan Rudolph: Part II: Amenable groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914236139044864 |
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| author | Downarowicz, Tomasz Thouvenot, Jean-Paul Weiss, Benjamin |
| author_facet | Downarowicz, Tomasz Thouvenot, Jean-Paul Weiss, Benjamin |
| contents | We prove an analog of Rudolph's theorem for actions of countable amenable groups, which asserts that among invariant measures with entropy at least c on the $G$-shift $(Λ^G,σ)$, a typical measure has entropy $c$ and is Bernoulli. We also address a relative version of this theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02939 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a theorem Dan Rudolph: Part II: Amenable groups Downarowicz, Tomasz Thouvenot, Jean-Paul Weiss, Benjamin Dynamical Systems Primary 37A05, 37A35, 43A07, Secondary 37A25, 37A15 We prove an analog of Rudolph's theorem for actions of countable amenable groups, which asserts that among invariant measures with entropy at least c on the $G$-shift $(Λ^G,σ)$, a typical measure has entropy $c$ and is Bernoulli. We also address a relative version of this theorem. |
| title | On a theorem Dan Rudolph: Part II: Amenable groups |
| topic | Dynamical Systems Primary 37A05, 37A35, 43A07, Secondary 37A25, 37A15 |
| url | https://arxiv.org/abs/2601.02939 |