A measure-conjugacy invariant for free group actions

Abstract

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.

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