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Means on equivalence relations

Kechris, Alexander S. and Miller, Benjamin D. (2008) Means on equivalence relations. Israel Journal of Mathematics, 163 (1). pp. 241-262. ISSN 0021-2172. doi:10.1007/s11856-008-0011-8.

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Suppose that X is a Polish space and E is a countable Borel equivalence relation on X. We show that if there is a Borel assignment of means to the equivalence classes of E, then E is smooth. We also show that if there is a Baire measurable assignment of means to the equivalence classes of E, then E is generically smooth.

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Additional Information:© 2008 Springer. Received December 17, 2004 and in revised form April 10, 2006. Research partially supported by NSF Grants DMS-9987437 and DMS-0455285. Research partially supported by NSF VIGRE Grant DMS-0502315. We would like to thank Vadim Kaimanovich for asking the question that led to this paper, Greg Hjorth for many interesting conversations along the way, and the anonymous referee for suggesting the current proof of Lemma 5.4 as a replacement for our original incorrect argument, and also for making several other useful suggestions.
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Subject Keywords:Equivalence Class; Equivalence Relation; Polish Space; Countable Group; Partial Transversal
Issue or Number:1
Record Number:CaltechAUTHORS:20130517-111643755
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Official Citation:Kechris, A. and B. Miller (2008). "Means on equivalence relations." Israel Journal of Mathematics 163(1): 241-262.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38559
Deposited By: Ruth Sustaita
Deposited On:22 May 2013 18:16
Last Modified:09 Nov 2021 23:38

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