Ergodic actions of countable groups and finite generating partitions

被引：6

作者：

Seward, Brandon ^{[1
]}

机构：

[1] Hebrew Univ Jerusalem, Einstein Inst Math, IL-91904 Jerusalem, Israel

来源：

GROUPS GEOMETRY AND DYNAMICS | 2015年 / 9卷 / 03期

基金：

美国国家科学基金会;

关键词：

Finite generator; generating partition; Shannon entropy; Krieger's finite generator theorem; ergodic; countable groups; f-invariant; sofic; MEASURE-PRESERVING TRANSFORMATIONS; SOFIC GROUPS; ENTROPY; INVARIANT;

D O I：

10.4171/GGD/328

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the following finite generator theorem. Let G be a countable group acting ergodically on a standard probability space. Suppose this action admits a generating partition having finite Shannon entropy. Then the action admits a finite generating partition. We also discuss relationships between generating partitions and f-invariant and sofic entropies.

引用

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页码：793 / 810

页数：18

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