Finite unions of equivalence relations
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- by John Kittrell PDF
- Proc. Amer. Math. Soc. 136 (2008), 3669-3673 Request permission
Abstract:
Say that a class of equivalence relations $\mathcal {C}$ has the finite union property if every equivalence relation that is the union of finitely many members of $\mathcal {C}$ must itself be a member of $\mathcal {C}$. Then the classes of hyperfinite, measure-amenable, Fréchet-amenable, and cheap equivalence relations have the finite union property.References
- Jacob Feldman and Calvin C. Moore, Ergodic equivalence relations, cohomology, and von Neumann algebras. I, Trans. Amer. Math. Soc. 234 (1977), no. 2, 289–324. MR 578656, DOI 10.1090/S0002-9947-1977-0578656-4
- S. Jackson, A. S. Kechris, and A. Louveau, Countable Borel equivalence relations, J. Math. Log. 2 (2002), no. 1, 1–80. MR 1900547, DOI 10.1142/S0219061302000138
- Alexander S. Kechris and Benjamin D. Miller, Topics in orbit equivalence, Lecture Notes in Mathematics, vol. 1852, Springer-Verlag, Berlin, 2004. MR 2095154, DOI 10.1007/b99421
Additional Information
- John Kittrell
- Affiliation: Knightsbridge Asset Management, LLC, Suite 460, 660 Newport Center Drive, Newport Beach, California 92660
- Email: jw.kittrell@gmail.com
- Received by editor(s): March 26, 2007
- Received by editor(s) in revised form: September 12, 2007
- Published electronically: May 19, 2008
- Communicated by: Julia Knight
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3669-3673
- MSC (2000): Primary 03E15; Secondary 03E20
- DOI: https://doi.org/10.1090/S0002-9939-08-09348-9
- MathSciNet review: 2415053