Groups, Geometry, and Dynamics

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Volume 5, Issue 3, 2011, pp. 663–672
DOI: 10.4171/GGD/142

Published online: 2011-06-18

Bernoulli actions and infinite entropy

David Kerr[1] and Hanfeng Li[2]

(1) Texas A&M University, College Station, USA
(2) SUNY at Buffalo, USA

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.

Keywords: Entropy, Bernoulli action, sofic group

Kerr David, Li Hanfeng: Bernoulli actions and infinite entropy. Groups Geom. Dyn. 5 (2011), 663-672. doi: 10.4171/GGD/142