Hausdorff content

Noun

• the d-dimensional Hausdorff content of S is defined by $C\_H^d(S):=\backslash lim\_\{\backslash sup\_i\; r\_i\; \backslash rightarrow\; 0\}\; \backslash inf\backslash Bigl\backslash \{\backslash sum\_i\; r\_i^d:\backslash text\{\; there\; is\; a\; cover\; of\; \}\; S\backslash text\{\; by\; balls\; with\; radii\; \}r\_i>0\backslash Bigr\backslash \}.$