Measurable equidecompositions via combinatorics and group theory

2014/08/08 by Łukasz Grabowski, Grabowski, Łukasz, András Máthé +3
Computer Science · Mathematics · #28Exx #Digital Image Processing Techniques #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Metric Geometry (math.MG) #math.MG #msc:28Exx

paper · pdf · doi:10.48550/arxiv.1408.1988

6 pages

arxiv created 2014/08/08 · openalex publication_date 2014/08/08 · arxiv updated 2014/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a sketch of proof that any two (Lebesgue) measurable subsets of the unit sphere in Rⁿ, for n≥ 3, with non-empty interiors and of the same measure are equidecomposable using pieces that are measurable.

Citations

• Sur la décomposition des ensembles de points en parties respectivement congruentes

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