Sofic entropy and amenable groups

Details Sofic entropy and amenable groups Sofic entropy and amenable groups

2010-08-07

arxiv.org/abs/1008.1354v2

Mathematics

Dynamical Systems

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Scientific paper

In previous work, I 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 $\sigma$-algebra.

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