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Definitioner

Substantiv

  1. the d-dimensional Hausdorff content of S is defined by C_H^d(S):=\lim_{\sup_i r_i \rightarrow 0} \inf\Bigl\{∑_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i>0\Bigr\}.

Exempel

  • 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.

Böjningsformer

PluralHausdorff contents

Kategorier