A measure-conjugacy invariant for free group actions

Mathematics – Dynamical Systems

Scientific paper

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The proofs in this version are slightly simpler than in the previous version. Also, the last 3 sections have been removed. I i

Scientific paper

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.

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