The Furstenberg lemma characterizes amenability
HTML articles powered by AMS MathViewer
- by Greg Hjorth
- Proc. Amer. Math. Soc. 134 (2006), 3061-3069
- DOI: https://doi.org/10.1090/S0002-9939-06-08321-3
- Published electronically: May 1, 2006
- PDF | Request permission
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
- T. Bates, MSc, Thesis, University of Ottawa, 1994.
- A. Connes, J. Feldman, and B. Weiss, An amenable equivalence relation is generated by a single transformation, Ergodic Theory Dynam. Systems 1 (1981), no. 4, 431–450 (1982). MR 662736, DOI 10.1017/s014338570000136x
- 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
- Wilfrid Hodges, Model theory, Encyclopedia of Mathematics and its Applications, vol. 42, Cambridge University Press, Cambridge, 1993. MR 1221741, DOI 10.1017/CBO9780511551574
- Robert J. Zimmer, Ergodic theory and semisimple groups, Monographs in Mathematics, vol. 81, Birkhäuser Verlag, Basel, 1984. MR 776417, DOI 10.1007/978-1-4684-9488-4
Bibliographic 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
- 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.
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 3061-3069
- MSC (2000): Primary 03E15, 37A20; Secondary 28A60, 03C15
- DOI: https://doi.org/10.1090/S0002-9939-06-08321-3
- MathSciNet review: 2231633