English

A measure-conjugacy invariant for free group actions

Dynamical Systems 2008-10-27 v2 Probability

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.

Keywords

Cite

@article{arxiv.0802.4294,
  title  = {A measure-conjugacy invariant for free group actions},
  author = {Lewis Bowen},
  journal= {arXiv preprint arXiv:0802.4294},
  year   = {2008}
}

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