Hausdorff content

noun1

1. •
   the d-dimensional Hausdorff content of S is defined by C_Hᵈ(S):= lim _(sup ᵢr_i→0) inf Bigl ∑ᵢr_iᵈ:thereisacoverofSbyballswithradiir_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.