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.

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Authors

Lewis Phylip Bowen

Mathematics Department
University of Hawaii at Manoa
2565 McCarthy Mall
Honolulu, HI 96822
United States
and
Mathematics Department
Mailstop 3368
Texas A&M University
College Station, TX 77843-3368
United States