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Sofic entropy and amenable groups

Published online by Cambridge University Press:  13 June 2011

LEWIS BOWEN
LEWIS BOWEN*
Affiliation:
Texas A&M University, Mailstop 3368, College Station, TX, 77843-3368, USA (email: lpbowen@math.tamu.edu)
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 2: Daniel J. Rudolph – in Memoriam , April 2012 , pp. 427 - 466
Copyright
Copyright © Cambridge University Press 2011

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