Hausdorff content

Noun

 * 1) the d-dimensional Hausdorff content of S is defined by $$C_H^d(S):=\lim_{\sup_i r_i \rightarrow 0} \inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i>0\Bigr\}.$$
 * The d-dimensional Hausdorff content of a set is a measure of the size of that set in the dth dimension.
 * The 0-dimensional Hausdorff content of a set is the number of points in that set.