AMENABILITY OF COUNTABLE GROUPS AND ACTIONS ON CANTOR SETS

Authors
GIORDANO T DELAHARPE P
Citation
T. Giordano et P. Delaharpe, AMENABILITY OF COUNTABLE GROUPS AND ACTIONS ON CANTOR SETS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 324(11), 1997, pp. 1255-1258
Citations number
14
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
324
Issue
11
Year of publication
1997
Pages
1255 - 1258
Database
ISI
SICI code
0764-4442(1997)324:11<1255:AOCGAA>2.0.ZU;2-#
Abstract
We answer a question of R. Grigorchuk by showing the following charact erization: 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 Gamm a-space is an equivariant subjective image of a Gamma-Cantor set.