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Results tagged with hausdorff-measure
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user 90512
Questions about Hausdorff measures, their variants (such as spherical Hausdorff measures) and generalisations.
5
votes
1
answer
708
views
The product of two Hausdorff measures
Let $(X,d_X)$ and $(Y,d_Y)$ be two compact metric space with Hausdorff dimensions $\dim_H(X)=n$ and $\dim_H(Y)=m$ and Hausdorff measures $\mathcal{H}^{n}$ and $\mathcal{H}^{m}$.
Assume that $\dim_H( …
- 1,799
5
votes
3
answers
355
views
Recovering the length metric from Hausdorff measure
The metric cannot be recovered from its Hausdorff measure in general. Now, assume that $(X,d_X)$ and $(Y, d_Y)$ are connected compact length spaces and induce $n$-dimensional Hausdorff measures $\mat …
- 1,799