Hausdorff measure
= Hausdorff measure
{c}
{title2=$\mathcal H^s$}
{wiki}
Hausdorff measure measures a <set> by the small-scale cost of covers, using the $s$th powers of their diameters and a standard normalization. In Euclidean dimension one, $\mathcal H^1$ agrees with arc length on <smooth> curves; in particular a line segment has its usual length.