Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


The Furstenberg lemma characterizes amenability

Author: Greg Hjorth
Journal: Proc. Amer. Math. Soc. 134 (2006), 3061-3069
MSC (2000): Primary 03E15, 37A20; Secondary 28A60, 03C15
Published electronically: May 1, 2006
MathSciNet review: 2231633
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We characterize amenability in terms of the existence of equivariant assignments of measures for cocycles into the homeomorphism group of a single compact metric space.

References [Enhancements On Off] (What's this?)

  • 1. T. Bates, MSc, Thesis, University of Ottawa, 1994.
  • 2. A. Connes, J. Feldman, and B. Weiss, An amenable equivalence relation is generated by a single transformation, Ergodic Theory Dynamical Systems 1 (1981), no. 4, 431–450 (1982). MR 662736 (84h:46090)
  • 3. Harry Furstenberg, Boundary theory and stochastic processes on homogeneous spaces, Harmonic analysis on homogeneous spaces (Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972) Amer. Math. Soc., Providence, R.I., 1973, pp. 193–229. MR 0352328 (50 #4815)
  • 4. Wilfrid Hodges, Model theory, Encyclopedia of Mathematics and its Applications, vol. 42, Cambridge University Press, Cambridge, 1993. MR 1221741 (94e:03002)
  • 5. Robert J. Zimmer, Ergodic theory and semisimple groups, Monographs in Mathematics, vol. 81, Birkhäuser Verlag, Basel, 1984. MR 776417 (86j:22014)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03E15, 37A20, 28A60, 03C15

Retrieve articles in all journals with MSC (2000): 03E15, 37A20, 28A60, 03C15

Additional Information

Greg Hjorth
Affiliation: Department of Mathematics, University of California Los Angeles, 405 Hilgard Avenue, Los Angeles, California 90095-1555

PII: S 0002-9939(06)08321-3
Keywords: Amenability, orbit equivalence, mean, homogeneous structure
Received by editor(s): January 14, 2005
Received by editor(s) in revised form: April 27, 2005
Published electronically: May 1, 2006
Additional Notes: This research was supported by NSF grant DMS 0140503
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia