Bi-Lipschitz Expansion of Measurable Sets
Abstract
We show that for 0<γ, γ' <1 and for measurable subsets of the unit square with Lebesgue measure γ there exist bi-Lipschitz maps with bounded Lipschitz constant (uniformly over all such sets) which are identity on the boundary and increases the Lebesgue measure of the set to at least 1-γ'.
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