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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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Absolute continuity of probability measures determined by dependence structure

We are on $\mathbb{R}^d$ with Borel $\sigma$-algebra. Let $\mu_1, ..., \mu_d$ be probability measures on $\mathbb{R}$ and $\Pi(\mu_1, \mu_2, ..., \mu_d)$ be the set of probability measures on $\mathbb …
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