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math.MG2016★ 18 cited
Measurable equidecompositions for group actions with an expansion property
Łukasz Grabowski, András Máthé, Oleg Pikhurko
Given an action of a group on a measure space , we provide a sufficient criterion under which two sets are measurably equidecomposable, i.e., can be pa…
math.MG2015
Measurable circle squaring
Łukasz Grabowski, András Máthé, Oleg Pikhurko
Laczkovich proved that if bounded subsets and of have the same non-zero Lebesgue measure and the box dimension of the boundary of each set is less than , then ther…
math.MG2014★ 1 cited
Measurable equidecompositions via combinatorics and group theory
Łukasz Grabowski, András Máthé, Oleg Pikhurko
We give a sketch of proof that any two (Lebesgue) measurable subsets of the unit sphere in , for , with non-empty interiors and of the same measure are equidecomposabl…