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arXiv · 1411.1510

Polish Models and Sofic Entropy

Ben Hayes
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Abstract

For actions of a sofic group on probability spaces, the entropy has been defined by Bowen, with an extension by Kerr-Li. In particular, when the action is by homeomorphisms of a compact space preserving a given measure, Kerr-Li show one can compute the measure-theoretic entropy in a manner which uses the topology of the space. We show how to compute the entropy of a an action of homeomorphisms of a Polish space preserving a given measure, also in a manner which uses the topology of the space. We give applications to spectral properties of actions with positive entropy, as well as for actions of completely positive entropy.

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Ben Hayes. 2015-12-31. Polish Models and Sofic Entropy. https://doi.org/10.1017/s1474748015000468

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