منابع مشابه
Borel circle squaring
We give a completely constructive solution to Tarski’s circle squaring problem. More generally, we prove a Borel version of an equidecomposition theorem due to Laczkovich. If k ≥ 1 and A,B ⊆ Rk are bounded Borel sets with the same positive Lebesgue measure whose boundaries have upper Minkowski dimension less than k, then A and B are equidecomposable by translations using Borel pieces. This answ...
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Laczkovich proved that if bounded subsets A and B of R 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, thi...
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ژورنال
عنوان ژورنال: Europhysics News
سال: 1993
ISSN: 0531-7479,1432-1092
DOI: 10.1051/epn/19932404071