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Questions about geometric properties of sets using measure theoretic techniques; rectifiability of sets and measures, currents, Plateau problem, isoperimetric inequality and related topics.
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Continuity of the Lebesgue measure w.r.t the Hausdorff metric
I have a question linked to Interplay of Hausdorff metric and Lebesgue measure. Let us denote as $\mathcal K(\mathbb R^n)$ the space of compact subsets of $\mathbb R^n$ endowed with the Hausdorff metr …