Category:Definitions/Hausdorff-Besicovitch Dimension
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This category contains definitions related to Hausdorff-Besicovitch Dimension.
Related results can be found in Category:Hausdorff-Besicovitch Dimension.
Let $F \subseteq \R^n$.
The Hausdorff-Besicovitch dimension of $F$ is defined as:
| \(\ds \map {\dim_H} F\) | \(:=\) | \(\ds \inf \set {s \in \R_{\ge 0} : \map {\HH^s} F = 0}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \sup \set {s \in \R_{\ge 0} : \map {\HH^s} F = +\infty}\) |
where $\map {\HH^s} \cdot$ denotes the $s$-dimensional Hausdorff measure on $\R^n$.
Pages in category "Definitions/Hausdorff-Besicovitch Dimension"
The following 3 pages are in this category, out of 3 total.