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:<math>\tau(C) = \mathrm{diam} (C)^s,\,</math>
where ''s'' is a positive constant and where ''τ'' is defined on the [[power set]] of all subsets of ''X'' (i.e., <math>\Sigma = 2^X</math>), the associated measure ''μ'' is the ''s''-dimensional [[Hausdorff measure]]. More generally, one could use any so-called [[dimension function]]. If instead ''τ'' is defined only on [[ball (mathematics)| ball]]s of ''X'', the associated measure <math>S^s</math> is an ''s''-dimensional spherical measure (not to be confused with the usual
<math>H^s(E) \le S^s(E) \le 2H^s(E)</math>.<ref name="Geometric Outer-Measures"/> {{clarify|reason=Covering by balls gives a different result than covering by general shapes; how this works needs to be explained in detail.}}
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