JournalsggdVol. 5, No. 3pp. 663–672

Bernoulli actions and infinite entropy

  • David Kerr

    Texas A&M University, College Station, USA
  • Hanfeng Li

    SUNY at Buffalo, USA
Bernoulli actions and infinite entropy cover
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Abstract

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.

Cite this article

David Kerr, Hanfeng Li, Bernoulli actions and infinite entropy. Groups Geom. Dyn. 5 (2011), no. 3, pp. 663–672

DOI 10.4171/GGD/142