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Measurable circle squaring
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Grabowski, Lukasz, Máthé, András and Pikhurko, Oleg (2017) Measurable circle squaring. Annals of Mathematics, 185 (2). pp. 671-710. doi:10.4007/annals.2017.185.2.6
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Official URL: http://dx.doi.org/10.4007/annals.2017.185.2.6
Abstract
Laczkovich proved that if bounded subsets A and B of ❘k have the same non-zero Lebesgue measure and the upper box dimension of the boundary of each set is less than k, then there is a partition of A into finitely many parts that can be translated to form a partition of B. Here we show that it can be additionally required that each part is both Baire and Lebesgue measurable. As special cases, this gives measurable and translation-only versions of Tarski’s circle squaring and Hilbert’s third problem.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Circle-squaring | ||||||
| Journal or Publication Title: | Annals of Mathematics | ||||||
| Publisher: | Mathematics Department, Princeton University | ||||||
| ISSN: | 0003-486X | ||||||
| Official Date: | 30 March 2017 | ||||||
| Dates: |
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| Volume: | 185 | ||||||
| Number: | 2 | ||||||
| Page Range: | pp. 671-710 | ||||||
| DOI: | 10.4007/annals.2017.185.2.6 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), Fondation Sciences Mathématiques de Paris, Leverhulme Trust (LT), Hungary. Nemzeti Kutatási és Technológiai Hivatal [National Office for Research and Technology] (NKFIH), European Research Council (ERC) | ||||||
| Grant number: | EP/K012045/1, EP/K012045/1 (EPSRC), 104178 (NKFIH), 306493 (ERC) | ||||||
| Open Access Version: |
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