Lexic.us

Definition of Hausdorff content

1. Noun. the ''d''-dimensional Hausdorff content of ''S'' is defined by $C\_H^d(S):=\backslash lim\_\{\backslash sup\_i\; r\_i\; \backslash rightarrow\; 0\}\; \backslash inf\backslash Bigl\backslash \{\backslash sum\_i\; r\_i^d:\backslash text\{\; there\; is\; a\; cover\; of\; \}\; S\backslash text\{\; by\; balls\; with\; radii\; \}r\_i>0\backslash Bigr\backslash \}.$ ¹

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