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Results tagged with hausdorff-measure
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user 454
Questions about Hausdorff measures, their variants (such as spherical Hausdorff measures) and generalisations.
5
votes
Accepted
The product of two Hausdorff measures
As noted in a comment, for Riemannian manifolds, the Hausdorff measures are equal to (up to a constant) the usual volumes. So this works.
The metric case you mention can fail. There are metric spac …
- 41.1k
7
votes
Accepted
Hausdorff measure
Not true for all $X$.
Taking the gauge function $\phi(t) = t^{1/2}/\log|t|$, construct a Cantor set $X$ in $\mathbb R$ using Hausdorff's original method so that $H^\phi(X) = 1$. Then the Hausdorff d …
- 41.1k
1
vote
Extending a $C^1$ function on $\mathbb R^n$ to a set of finite $\mathcal H^{n-2}$ measure
You are extending from an open set.
Related, but different, extending from a closed set:
There is a paper of H. Whitney on defining the concept $C^k$ for a function defined on a closed subset of $\mat …
- 41.1k