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Results tagged with hausdorff-dimension
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user 121665
Questions about dimensions of possibly highly irregular or "rough" sets, Hausdorff–Besicovitch dimension and related concepts such as box-counting or Minkowski–Bouligand dimension.
15
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4
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Steinhaus theorem and Hausdorff dimension
Assume for simplicity that sets $A_i\subset\mathbb{R}$ are compact. If $A_1$ and $A_2$ have positive length, then $A_1+A_2$ contains an interval. That is a variant of the classical Steinhaus theorem a …
- 28k
11
votes
1
answer
953
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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