Measurable circle squaring

• 成果类型: Article
• 署名作者: Grabowski, Lukasz; Mathe, Andras; Pikhurko, Oleg
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.185.2.6
• 发表日期: 2017
• 页码: 671-710
• 关键词: sets; equidecomposability; DECOMPOSITION; discrepancy; convex

摘要

Laczkovich proved that if bounded subsets A and B of R-k have the same nonzero 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.