Hausdorff content
Noun
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Noun
Hausdorff content (plural Hausdorff contents)
- 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.
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