Hausdorff content

English

Noun

1. the d-dimensional Hausdorff content of S is defined by $C_H^d(S):=\underset{\underset{i}{\sup }{r}_i\to 0}{\lim }\inf \{\sum _i{r}_i^d:\text{ there is a cover of }S\text{ by balls with radii }{r}_i>0\}.$

   The d-dimensional Hausdorff content of a set is a measure of the size of that set in the d^th dimension.

   The 0-dimensional Hausdorff content of a set is the number of points in that set.

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