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Measurable equidecompositions for group actions with an expansion property
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Grabowski, Lukasz, Máthé, András and Pikhurko, Oleg (2022) Measurable equidecompositions for group actions with an expansion property. Journal of the European Mathematical Society, 24 (12). pp. 4277-4326. doi:10.4171/JEMS/1189 ISSN 1435-9855.
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Official URL: https://doi.org/10.4171/JEMS/1189
Abstract
Given an action of a group Γ on a measure space Ω, we provide a sufficient criterion under which two sets A,B⊆Ω are measurably equidecomposable, i.e., A can be partitioned into finitely many measurable pieces which can be rearranged using the elements of Γ to form a partition of B. In particular, we prove that every bounded measurable subset of Rn, n≥3, with non-empty interior is measurably equidecomposable to a ball via isometries. The analogous result also holds for some other spaces, such as the sphere or the hyperbolic space of dimension n≥2.
| 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): | Euclid's Elements, Geometry, Geometry, Plane, Lie groups, Measure theory | ||||||||||||||||||
| Journal or Publication Title: | Journal of the European Mathematical Society | ||||||||||||||||||
| Publisher: | European Mathematical Society Publishing House | ||||||||||||||||||
| ISSN: | 1435-9855 | ||||||||||||||||||
| Official Date: | 9 October 2022 | ||||||||||||||||||
| Dates: |
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| Volume: | 24 | ||||||||||||||||||
| Number: | 12 | ||||||||||||||||||
| Page Range: | pp. 4277-4326 | ||||||||||||||||||
| DOI: | 10.4171/JEMS/1189 | ||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||
| Copyright Holders: | © 2020 EMS | ||||||||||||||||||
| Date of first compliant deposit: | 21 September 2020 | ||||||||||||||||||
| Date of first compliant Open Access: | 21 September 2020 | ||||||||||||||||||
| RIOXX Funder/Project Grant: |
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