Sofic entropy and amenable groups

被引：44

作者：

Bowen, Lewis ^{[1
]}

机构：

[1] Texas A&M Univ, College Stn, TX 77843 USA

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2012年 / 32卷

基金：

美国国家科学基金会;

关键词：

MEASURE PRESERVING TRANSFORMATIONS;

D O I：

10.1017/S0143385711000253

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 sigma-algebra.

引用

页码：427 / 466

页数：40

共 20 条

[1]

Bowen L., ERGOD TH DY IN PRESS

[2] MEASURE CONJUGACY INVARIANTS FOR ACTIONS OF COUNTABLE SOFIC GROUPS [J].