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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.

27 votes
3 answers
6k views

Is arbitrary union of closed balls in $\mathbb{R}^n$ Lebesgue measurable?

Is an arbitrary union of non-trivial closed balls in the Euclidean space $\mathbb{R}^n$ Lebesgue measurable? If so, is it a Borel set? @George I still have two questions concerning your sketch of pr …
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