Sofic entropy and amenable groups

In previous work, the author introduced a measure-conjugacy invariant for sofic group actions called sofic entropy. Here, it is proven that the sofic entropy of an amenable group action equals its classical entropy. The proof uses a new measure-conjugacy invariant called upper-sofic entropy and a th...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2012-04, Vol.32 (2), p.427-466
Main Author: BOWEN, LEWIS
Format: Article
Language:English
Subjects:
Algebra
Dynamical systems
Entropy
Ergodic processes
Invariants
Mathematics
Orbits
Proving
Theorems
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Summary:In previous work, the author introduced a measure-conjugacy invariant for sofic group actions called sofic entropy. Here, it is proven that the sofic entropy of an amenable group action equals its classical entropy. The proof uses a new measure-conjugacy invariant called upper-sofic entropy and a theorem of Rudolph and Weiss for the entropy of orbit-equivalent actions relative to the orbit change σ-algebra.
ISSN:0143-3857
1469-4417
DOI:10.1017/S0143385711000253