Definition:Hausdorff-Besicovitch Dimension

Definition
Let $\R^n$ be the $n$-dimensional Euclidean space.

Let $F \subseteq \R^n$.

The Hausdorff-Besicovitch dimension of $F$ is defined as:

where $\map {\HH^s} F$ denotes the $s$-dimensional Hausdorff measure on $\R^n$ of $F$.

Also known as
This is also known as the Hausdorff dimension.

Also see

 * Hausdorff Dimension is Well-Defined : In particular, it is shown that $\map {\dim_H} F \in \closedint 0 n$.
 * Definition:Box-counting Dimension
 * Definition:Packing Dimension