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

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Hausdorff measure and the volume form

There are two tools, generalizing a concept of a volume to the case of submanifolds in $\mathbb{R}^n$, namely the Hausdorff measure $H^k$ and the volume form. The question is how to show that if $M$ i …