Measurable equidecompositions via combinatorics and group theory
Łukasz Grabowski, András Máthé, Oleg Pikhurko · arXiv (Cornell University) · 2014
We give a sketch of proof that any two (Lebesgue) measurable subsets of the unit sphere in $R^n$, for $n\ge 3$, with non-empty interiors and of the same measure are equidecomposable using pieces that are measurable.