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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
Posted:
May 1, 2006
MathSciNet review:
2231633
Full-text PDF Free Access
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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
- 1.
T. Bates, MSc, Thesis, University of Ottawa, 1994.
- 2.
A. Connes, J. Feldman, B. Weiss, An amenable equivalence relation is generated by a single transformation, Journal of Ergodic Theory and Dynamical Systems, vol. 1(1981), pp. 431-450. MR 0662736 (84h:46090)
- 3.
H. Furstenberg, Boundary theory and stochastic processes on homogeneous spaces in Harmonic analysis on homogeneous spaces, in Symposia on pure and applied math, Williamstown, 1972, Proceedings vol. 26(1973), pp. 193-229. MR 0352328 (50:4815)
- 4.
W. Hodges, Model Theory, Cambridge University Press, Cambridge, 1993. MR 1221741 (94e:03002)
- 5.
R. Zimmer, Ergodic theory and semi-simple groups, Birkhauser, Basel, 1984. MR 0776417 (86j:22014)
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Additional Information
Greg Hjorth
Affiliation:
Department of Mathematics, University of California Los Angeles, 405 Hilgard Avenue, Los Angeles, California 90095-1555
Email:
greg@math.ucla.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08321-3
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
Posted:
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 after
28 years from publication.
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