Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Finite unions of equivalence relations

Author: John Kittrell
Journal: Proc. Amer. Math. Soc. 136 (2008), 3669-3673
MSC (2000): Primary 03E15; Secondary 03E20
Published electronically: May 19, 2008
MathSciNet review: 2415053
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

  • 1. J. Feldman and C.C. Moore, Ergodic equivalence relations and von Neumann algebras, I, Trans. Amer. Math. Soc. 234 (1977), 289-324. MR 0578656 (58:28261a)
  • 2. S. Jackson, A.S. Kechris, A. Louveau, Countable Borel equivalence relations, J. Math. Logic 2(1) (2002), 1-80. MR 1900547 (2003f:03066)
  • 3. A.S. Kechris, B.D. Miller, Topics in orbit equivalence, Springer, 2004. MR 2095154 (2005f:37010)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03E15, 03E20

Retrieve articles in all journals with MSC (2000): 03E15, 03E20

Additional Information

John Kittrell
Affiliation: Knightsbridge Asset Management, LLC, Suite 460, 660 Newport Center Drive, Newport Beach, California 92660

Keywords: Countable Borel equivalence relations, hyperfinite equivalence relations, union problems
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society