# Hausdorff metric

1. (analysis) In the abstract metric space of all compact subsets of ${\displaystyle \mathbb {R} ^{n}}$, given a pair of compact sets A and B, the Hausdorff metric is ${\displaystyle h(A,B)={\mbox{max}}\{\rho (A,B),\rho (B,A)\}}$ where ${\displaystyle \rho (A,B)=\sup _{a\in A}\inf _{b\in B}\,d(a,b)}$, where d is the Euclidean metric in ${\displaystyle \mathbb {R} ^{n}}$.