Lewis Bowen
Published 2008-02-28, updated 2008-10-26Version 2
This paper introduces a new measure-conjugacy invariant for actions of free groups. Using this invariant, it is shown that two Bernoulli shifts over a finitely generated free group are measurably conjugate if and only if their base measures have the same entropy. This answers a question of Ornstein and Weiss.
Comments: The proofs in this version are slightly simpler than in the previous version. Also, the last 3 sections have been removed. I intend to write up the main results of those sections in a separate paper
Bernoulli shifts with bases of equal entropy are isomorphic
Sofic entropy and amenable groups
The ergodic theory of free group actions: entropy and the f-invariant
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