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arXiv · 1503.02827

Zero-dimensional extensions of amenable group actions

Dawid Huczek
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Abstract

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 $μ$ on $X$ has exactly one preimage $ν$ on $Y$ and the conditional entropy of $ν$ 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.

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Dawid Huczek. 2019-02-03. Zero-dimensional extensions of amenable group actions. https://arxiv.org/abs/1503.02827

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