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Questions about Hausdorff measures, their variants (such as spherical Hausdorff measures) and generalisations.

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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 …
Martin Väth's user avatar
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