Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published 2008 | Published
Journal Article Open

Amenable actions and almost invariant sets

Abstract

In this paper, we study the connections between properties of the action of a countable group Γ on a countable set X and the ergodic theoretic properties of the corresponding generalized Bernoulli shift, i.e., the corresponding shift action of Γ on M^X, where M is a measure space. In particular, we show that the action of Γ on X is amenable iff the shift Γ → M^X has almost invariant sets.

Additional Information

© 2007 American Mathematical Society. Received by editor(s): October 2, 2006. Received by editor(s) in revised form: February 8, 2007. Posted: November 3, 2007. Additional Notes: This research was partially supported by NSF grant DMS-0455285. Communicated by: Jane M. Hawkins.

Attached Files

Published - KECpams08.pdf

Files

KECpams08.pdf
Files (196.7 kB)
Name Size Download all
md5:410e676a722bed3aed43a35c34d3e03a
196.7 kB Preview Download

Additional details

Created:
August 22, 2023
Modified:
March 5, 2024