Hausdorff distance

Summary

The Hausdorff distance measures how far two subsets of a metric space are from each other. It is the smallest $\varepsilon$ such that each set lies in the $\varepsilon$-neighbourhood of the other. On the nonempty compact subsets of a metric space it is a metric. With it, the compact convex sets of $\R^n$ form the basic space of convex geometry.