Measurable Equidecompositions via Combinatorics and Group Theory

Abstract

We give a sketch of proof that any two (Lebesgue) measurable subsets of the unit sphere in R, for n ≥ 3, with non-empty interiors and of the same measure are equidecomposable using pieces that are measurable. Recall that two subsets A and B of R are equidecomposable if for some m∈N there exist isometries γ1, . . . , γm and partitions A = A1 t · · · t Am and… (More)

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Cite this paper

@inproceedings{Grabowski2014MeasurableEV, title={Measurable Equidecompositions via Combinatorics and Group Theory}, author={Łukasz Grabowski and Andr{\'a}s M{\'a}th{\'e} and Oleg Pikhurko}, year={2014} }