Published January 2008
| Version public
Journal Article
Means on equivalence relations
Creators
Abstract
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.
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.Additional details
Identifiers
- Eprint ID
- 38559
- Resolver ID
- CaltechAUTHORS:20130517-111643755
Funding
- NSF
- DMS-9987437
- NSF
- DMS-0455285
- NSF
- DMS-0502315
Dates
- Created
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2013-05-22Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field
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- Mathematics Department