Minkowski content

Summary

The Minkowski content measures the $m$-dimensional size of a subset of $\R^n$ through the volume of its thin neighbourhoods. One thickens the set by $r$, takes the Lebesgue measure of the result, and divides by the volume of an $(n-m)$-dimensional ball of radius $r$. For nice sets it gives length, area and volume, and for rough sets it is linked to the box-counting dimension.