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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 ISSN 0003-486X.

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Official URL: http://dx.doi.org/10.4007/annals.2017.185.2.6

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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:
DateEvent
30 March 2017Published
24 August 2016Accepted
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
Date of first compliant deposit: 13 September 2016
Date of first compliant Open Access: 3 May 2017
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)
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