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Results tagged with hausdorff-dimension
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user 51695
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
Maximal Hausdorff dimension of the set on which derivatives do not agree
If by not agree you include that the derivative may not exist, you can get any dimension and measure that does not contradict the almost everywhere. Consider the worst case $d=1$:
Take the constructio …
- 2,504
5
votes
Accepted
Hausdorff dimension of the zero set of $\nabla f$
Checking this in perfect detail might be a bit technical, but the following looks like it could work for any dimension up to n:
For 1d: Take an S curve $\phi: [0,1] \to [0,1]$ such that $\phi(0) = 0$, …
- 2,504
3
votes
Accepted
Hausdorff dimension of the zero set of the gradient of an eikonal function
Building on Pietro Majer's answer to you previous question for a change, consider the following:
Let $g: [0,\infty) \to \mathbb{R}$ be the unique continuous function such that $g(0)=0$, $g'(x) = 1$ fo …
- 2,504