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Results tagged with geometric-measure-theory
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user 165275
Questions about geometric properties of sets using measure theoretic techniques; rectifiability of sets and measures, currents, Plateau problem, isoperimetric inequality and related topics.
6
votes
Accepted
Disjoint union of closed sets
Yes, sure: If you have a finite union of closed intervals, the complement in [0,1] is a finite union of open (in [0,1]) intervals. Hence, you find in this complement a finite union of closed intervals …
- 1,869
9
votes
Accepted
Finiteness of Hausdorff measure of balls
As a counterexample, let $X$ be an infinite-dimensional normed space. For $\varepsilon<r/2$ it follows from Borsuk-Ulam that you need more than $n$ closed sets of diameter $\varepsilon$ to cover the i …
- 1,869