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Measurable circle squaring

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Measurable circle squaring. / Grabowski, Łukasz; Máthé, András; Pikhurko, Oleg.
In: Annals of Mathematics, Vol. 185, No. 2, 31.03.2017, p. 671-710.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Grabowski, Ł, Máthé, A & Pikhurko, O 2017, 'Measurable circle squaring', Annals of Mathematics, vol. 185, no. 2, pp. 671-710. https://doi.org/10.4007/annals.2017.185.2.6

APA

Grabowski, Ł., Máthé, A., & Pikhurko, O. (2017). Measurable circle squaring. Annals of Mathematics, 185(2), 671-710. https://doi.org/10.4007/annals.2017.185.2.6

Vancouver

Grabowski Ł, Máthé A, Pikhurko O. Measurable circle squaring. Annals of Mathematics. 2017 Mar 31;185(2):671-710. Epub 2017 Mar 1. doi: 10.4007/annals.2017.185.2.6

Author

Grabowski, Łukasz ; Máthé, András ; Pikhurko, Oleg. / Measurable circle squaring. In: Annals of Mathematics. 2017 ; Vol. 185, No. 2. pp. 671-710.

Bibtex

@article{54628ed5832c4a2fbba92c26b98190a3,
title = "Measurable circle squaring",
abstract = "Laczkovich proved that if bounded subsets $A$ and $B$ of $R^k$ have the same non-zero Lebesgue measure and the 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.",
keywords = "math.MG, math.CO, Equidecomposition, Graph matching, Measurability, Tarski's circle squaring",
author = "{\L}ukasz Grabowski and Andr{\'a}s M{\'a}th{\'e} and Oleg Pikhurko",
note = "40 pages; Lemma 4.4 improved & more details added; accepted by Annals of Mathematics",
year = "2017",
month = mar,
day = "31",
doi = "10.4007/annals.2017.185.2.6",
language = "English",
volume = "185",
pages = "671--710",
journal = "Annals of Mathematics",
issn = "0003-486X",
publisher = "Princeton University Press",
number = "2",

}

RIS

TY - JOUR

T1 - Measurable circle squaring

AU - Grabowski, Łukasz

AU - Máthé, András

AU - Pikhurko, Oleg

N1 - 40 pages; Lemma 4.4 improved & more details added; accepted by Annals of Mathematics

PY - 2017/3/31

Y1 - 2017/3/31

N2 - Laczkovich proved that if bounded subsets $A$ and $B$ of $R^k$ have the same non-zero Lebesgue measure and the 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.

AB - Laczkovich proved that if bounded subsets $A$ and $B$ of $R^k$ have the same non-zero Lebesgue measure and the 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.

KW - math.MG

KW - math.CO

KW - Equidecomposition

KW - Graph matching

KW - Measurability

KW - Tarski's circle squaring

U2 - 10.4007/annals.2017.185.2.6

DO - 10.4007/annals.2017.185.2.6

M3 - Journal article

VL - 185

SP - 671

EP - 710

JO - Annals of Mathematics

JF - Annals of Mathematics

SN - 0003-486X

IS - 2

ER -