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Local and doubly empirical convergence and the entropy of algebraic actions of sofic groups

  • BEN HAYES (a1)

Abstract

Let $G$ be a sofic group and $X$ a compact group with $G\curvearrowright X$ by automorphisms. Using (and reformulating) the notion of local and doubly empirical convergence developed by Austin, we show that in many cases the topological and the measure-theoretic entropy with respect to the Haar measure of $G\curvearrowright X$ agree. Our method of proof recovers all known examples. Moreover, the proofs are direct and do not go through explicitly computing the measure-theoretic or topological entropy.

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Local and doubly empirical convergence and the entropy of algebraic actions of sofic groups

  • BEN HAYES (a1)

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