Amenability of countable groups and actions on Cantor sets

被引：6

作者：

Giordano, T ^{[1
]}

delaHarpe, P ^{[1
]}

机构：

[1] SECT MATH,CH-1211 GENEVA 24,SWITZERLAND

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 1997年 / 324卷 / 11期

关键词：

D O I：

10.1016/S0764-4442(99)80409-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We answer a question of R. Grigorchuk by showing the following characterization: for a countable group Gamma to be amenable, it is necessary and sufficient that any continuous action of Gamma on the Canter set has an invariant probability measure. The proof uses an easy variation of a classical result of Alexandroff and Urysohn: any metrisable Gamma-space is an equivariant subjective image of a Gamma-Cantor set.

引用

页码：1255 / 1258

页数：4

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