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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On measures ergodic with respect to
an analytic equivalence relation


Authors: Alain Louveau and Gabriel Mokobodzki
Journal: Trans. Amer. Math. Soc. 349 (1997), 4815-4823
MSC (1991): Primary 04A15, 28D99
MathSciNet review: 1451609
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we prove that the set of probability measures which are ergodic with respect to an analytic equivalence relation is an analytic set. This is obtained by approximating analytic equivalence relations by measures, and is used to give an elementary proof of an ergodic decomposition theorem of Kechris.


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

  • [D] A. Ditzen, Definable equivalence relations on Polish spaces, Ph.D. Thesis, Caltech (1992).
  • [Ke] A.S. Kechris, Lectures on definable group actions and equivalence relations, forthcoming monograph.
  • [KL] Alexander S. Kechris and Alain Louveau, Descriptive set theory and the structure of sets of uniqueness, London Mathematical Society Lecture Note Series, vol. 128, Cambridge University Press, Cambridge, 1987. MR 953784
  • [Kr] Ulrich Krengel, Ergodic theorems, de Gruyter Studies in Mathematics, vol. 6, Walter de Gruyter & Co., Berlin, 1985. With a supplement by Antoine Brunel. MR 797411

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Additional Information

Alain Louveau
Affiliation: Equipe d’Analyse, Université Paris VI, 75230 Paris Cedex 5, France
Email: louveau@ccr.jussieu.fr

Gabriel Mokobodzki
Affiliation: Equipe d’Analyse, Université Paris VI, 75230 Paris Cedex 5, France
Email: gam@jussieu.fr

DOI: https://doi.org/10.1090/S0002-9947-97-02070-9
Keywords: Analytic equivalence relation, ergodic measure, ergodic decomposition
Received by editor(s): June 9, 1995
Article copyright: © Copyright 1997 American Mathematical Society