or, more generally, in any metric space.

The zero-dimensional Hausdorff measure is the number of points in the set (if the set is finite) or ? if the set is infinite. Likewise, the one-dimensional Hausdorff measure of a simple curve in is equal to the length of the curve, and the two-dimensional Hausdorff measure of a Lebesgue-measurable subset of is proportional to the area of the set. Thus, the concept of the Hausdorff