On measures ergodic with respect to an analytic equivalence relation
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- by Alain Louveau and Gabriel Mokobodzki PDF
- Trans. Amer. Math. Soc. 349 (1997), 4815-4823 Request permission
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
- A. Ditzen, Definable equivalence relations on Polish spaces, Ph.D. Thesis, Caltech (1992).
- A.S. Kechris, Lectures on definable group actions and equivalence relations, forthcoming monograph.
- 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, DOI 10.1017/CBO9780511758850
- 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, DOI 10.1515/9783110844641
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
- Received by editor(s): June 9, 1995
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 4815-4823
- MSC (1991): Primary 04A15, 28D99
- DOI: https://doi.org/10.1090/S0002-9947-97-02070-9
- MathSciNet review: 1451609