We show that, for countable sofic groups, a Bernoulli action with infinite entropy base has infinite entropy with respect to every sofic approximation sequence. This builds on the work of Lewis Bowen in the case of finite entropy base and completes the computation of measure entropy for Bernoulli actions over countable sofic groups. One consequence is that such a Bernoulli action fails to have a generating countable partition with finite entropy if the base has infinite entropy, which in the amenable case is well known and in the case that the acting group contains the free group on two generators was established by Bowen.
@article{10_4171_ggd_142,
author = {David Kerr and Hanfeng Li},
title = {Bernoulli actions and infinite entropy},
journal = {Groups, geometry, and dynamics},
pages = {663--672},
year = {2011},
volume = {5},
number = {3},
doi = {10.4171/ggd/142},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/142/}
}
TY - JOUR
AU - David Kerr
AU - Hanfeng Li
TI - Bernoulli actions and infinite entropy
JO - Groups, geometry, and dynamics
PY - 2011
SP - 663
EP - 672
VL - 5
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/142/
DO - 10.4171/ggd/142
ID - 10_4171_ggd_142
ER -
%0 Journal Article
%A David Kerr
%A Hanfeng Li
%T Bernoulli actions and infinite entropy
%J Groups, geometry, and dynamics
%D 2011
%P 663-672
%V 5
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/142/
%R 10.4171/ggd/142
%F 10_4171_ggd_142
