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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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Decomposition of non negative Radon measure into $L^1$ and $H^{-1}$ functions

You can find both results in Theorems 2.1 and 2.4 in Lucio Boccardo, Thierry Gallouët, Luigi Orsina, Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, …
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