- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:59
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
5
2011
3
Bernoulli actions and infinite entropy
David
Kerr
Texas A&M University, COLLEGE STATION, UNITED STATES
Hanfeng
Li
SUNY at Buffalo, BUFFALO, UNITED STATES
Entropy, Bernoulli action, sofic group
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.
Dynamical systems and ergodic theory
General
663
672
10.4171/GGD/142
http://www.ems-ph.org/doi/10.4171/GGD/142