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Results tagged with hausdorff-dimension
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user 103792
Questions about dimensions of possibly highly irregular or "rough" sets, Hausdorff–Besicovitch dimension and related concepts such as box-counting or Minkowski–Bouligand dimension.
4
votes
Accepted
Hausdorff dimension of the non-differentiability set of a locally Lipschitz function
You can't find a reference because it's false. Rademacher's theorem (Lebesgue-almost everywhere differentiability) is the best one can do.
In fact, for every Lebesgue-null set $E \subset \mathbf{R}$, …
- 5,048
3
votes
Accepted
Hausdorff dimension of the non-differentiability set a convex function
I just stumbled across your question. I have no idea how the proofs of these results go—and I am inclined to believe that they would indeed also prove the version you seek—but here's a way to deduce t …
- 5,048
3
votes
Accepted
Hausdorff dimension and non-empty intersections with lines
This is true if the dimension of $A$ is strictly larger than $d-1$; on the other hand taking $A = \{ x^d = 0 \}$ shows that $s = d-1$ is not enough. To prove the first claim we use the co-area formula …
- 5,048