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σ-Lacunary actions of Polish groups
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Grebík, Jan (2020) σ-Lacunary actions of Polish groups. Proceedings of the American Mathematical Society, 148 (8). pp. 3583-3589. doi:10.1090/proc/14982 ISSN 0002-9939.
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Official URL: http://dx.doi.org/10.1090/proc/14982
Abstract
We show that every essentially countable orbit equivalence relation induced by a continuous action of a Polish group on a Polish space is $ \sigma $-lacunary. In combination with Gao and Jackson [Invent. Math. 201 (2015), pp. 309-383] we obtain a straightforward proof of the result from Ding and Gao [Adv. Math. 307 (2017), pp. 312-343] that every essentially countable equivalence relation that is induced by an action of an abelian nonarchimedean Polish group is Borel reducible to $ \mathbb{E}_0$, i.e., it is essentially hyperfinite.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Polish spaces (Mathematics) | ||||||||||||
| Journal or Publication Title: | Proceedings of the American Mathematical Society | ||||||||||||
| Publisher: | American Mathematical Society | ||||||||||||
| ISSN: | 0002-9939 | ||||||||||||
| Official Date: | 17 March 2020 | ||||||||||||
| Dates: |
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| Volume: | 148 | ||||||||||||
| Number: | 8 | ||||||||||||
| Page Range: | pp. 3583-3589 | ||||||||||||
| DOI: | 10.1090/proc/14982 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Reuse Statement (publisher, data, author rights): | “First published in Proceedings of the American Mathematical Society, 2020, 148(8), published by the American Mathematical Society,” and the copyright notice in proper form must be placed on all copies. | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| Copyright Holders: | © Copyright 2020 American Mathematical Society | ||||||||||||
| Date of first compliant deposit: | 10 July 2020 | ||||||||||||
| Date of first compliant Open Access: | 15 July 2020 | ||||||||||||
| RIOXX Funder/Project Grant: |
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