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Soficity, amenability, and dynamical entropy
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 135, Number 3, June 2013
- pp. 721-761
- 10.1353/ajm.2013.0024
- Article
- Additional Information
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In a previous paper the authors developed an operator-algebraic approach to Lewis
Bowen's sofic measure entropy that yields invariants for actions of countable sofic
groups by homeomorphisms on a compact metrizable space and by measure-preserving
transformations on a standard probability space. We show here that these measure and
topological entropy invariants both coincide with their classical counterparts when
the acting group is amenable.