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Results tagged with hausdorff-dimension
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user 15780
Questions about dimensions of possibly highly irregular or "rough" sets, Hausdorff–Besicovitch dimension and related concepts such as box-counting or Minkowski–Bouligand dimension.
8
votes
Accepted
How can dimension depend on the point?
Lars Olsen [1], [2] (2005, 2005) has proved some results about this notion. Let $E \subseteq {\mathbb R}^{n}$ and $x \in {\mathbb R}^{n},$ where $n$ is a fixed positive integer. Let $\dim_{H}(E,x)$ an …
- 3,312
8
votes
Accepted
How large can the set of turbulent points be?
The Hausdorff dimension of the turbulent points can be $n.$
For $n=1$ (the reals), this is a consequence of the proof of Theorem 1 in On Lebesgue’s density theorem by Casper Goffman (1950):
THEOREM 1 …
- 3,312