Zero-dimensional extensions of amenable group actions
| Autor: | Dawid Huczek |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Conditional entropy
Pure mathematics Group (mathematics) 37A35 37B40 General Mathematics Amenable group Zero (complex analysis) Extension (predicate logic) Dynamical Systems (math.DS) Measure (mathematics) FOS: Mathematics Countable set Mathematics - Dynamical Systems Dynamical system (definition) Mathematics |
| DOI: | 10.48550/arxiv.1503.02827 |
| Popis: | We prove that every dynamical system $X$ with free action of a countable amenable group $G$ by homeomorphisms has a zero-dimensional extension $Y$ which is faithful and principal, i.e. every $G$-invariant measure $\mu$ on $X$ has exactly one preimage $\nu$ on $Y$ and the conditional entropy of $\nu$ with respect to $X$ is zero. This is a version of an earlier result by T. Downarowicz and D. Huczek, which establishes the existence of zero-dimensional principal and faithful extensions for general actions of the group of integers. Comment: 19 pages, 7 figures |
| Databáze: | OpenAIRE |
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