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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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Doubling metrics, doubling measures, Lebesgue density

A version of Lebesgue differentiation for non-doubling measures on doubling metric space appears in section 3 of: T. Hytonen, A FRAMEWORK FOR NON-HOMOGENEOUS ANALYSIS ON METRIC SPACES, AND THE RBMO S …
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