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Results tagged with hausdorff-measure
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user 121665
Questions about Hausdorff measures, their variants (such as spherical Hausdorff measures) and generalisations.
11
votes
1
answer
953
views
Coarea inequality, Eilenberg inequality
The general statement of the coarea inequality known also as the Eilenberg inequality is:
Theorem. If $f:X\to Y$ is a Lipschitz map between metric spaces and $A\subset X$, $0\leq m\leq n$, then $$
\ …
- 28k
16
votes
0
answers
611
views
Isoperimetric inequality and geometric measure theory
The following version of the isoperimetric inequality can be easily deduced from the Brunn-Minkowski inequality:
Theorem. If $K\subset\mathbb{R}^n$ is compact, then $$ |K|^{\frac{n-1}{n}}\leq n^{- …
- 28k