Article contents
Local and doubly empirical convergence and the entropy of algebraic actions of sofic groups
Published online by Cambridge University Press: 07 September 2017
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.
- Type
- Original Article
- Information
- Copyright
- © Cambridge University Press, 2017
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20190226003025227-0638:S0143385717000694:S0143385717000694_inline5.gif?pub-status=live)
- 1
- Cited by