# Hausdorff metric

### From Glossary

This metric arises in normed spaces, giving a measure of distance between two (point) sets, and . Given a norm, let be the distance function between a point and a set:

Define

Then, is the Hausdorff metric. In words, this says that for each , let be its closest point in . Then, maximize this distance among all .

For example, let be the interval, , and let be the interval, . The Hausdorff distance between these two intervals is: