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Results tagged with hausdorff-dimension
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user 9652
Questions about dimensions of possibly highly irregular or "rough" sets, Hausdorff–Besicovitch dimension and related concepts such as box-counting or Minkowski–Bouligand dimension.
11
votes
1
answer
1k
views
Geometric measures different from Hausdorff
$\newcommand{\RR}{\mathbb{R}}\newcommand{\calF}{\mathcal{F}}\newcommand{\diam}{\mathrm{diam}}$
In geometric measure theory there are various notions of $m$-dimensional measure for sets $A\subset \RR^n …
- 12.7k
8
votes
1
answer
201
views
How do sets with unit fractional Hausdorff measure of dimension $>1$ look like?
Triggered by the recent question How can we not know the measure of the Sierpiński triangle? I would like to ask:
Let $s>1$ and $s$ not be an integer. How to construct a set $A$ with $\mathfrak{H}^s( …
- 12.7k