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Results tagged with hausdorff-dimension
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user 44463
Questions about dimensions of possibly highly irregular or "rough" sets, Hausdorff–Besicovitch dimension and related concepts such as box-counting or Minkowski–Bouligand dimension.
2
votes
Accepted
Hausdorff dimension and $W^{1,1}$ functions
If $f$ is Lipschitz then $\dim_H f(A) \le \dim_H A$, since $H^s_\delta(f(A)) \le Lip(f) \cdot H^s_\delta(A)$ for any $\delta>0$.
However there exists an absolutely continuous function $f\in W^{1,1}$ …
- 1,277
14
votes
Accepted
Existence of subset with given Hausdorff dimension
First of all, $\dim_{H} (A) = \alpha$ iff $ H^k(A)=\infty$ for all $k<\beta$ and $H^k(A) = 0$ for all $k>\beta$. Then $H^\alpha(A) = \infty$ for all $\alpha \in (0,\beta)$.
If $A$ is closed then by …
- 1,277