Definition:Hausdorff Metric
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Definition
Let $M = \struct {S, d}$ be a metric space.
Let $\CC$ be the set of compact subsets of $M$.
Let $\d: \CC \times \CC \to \R_{\ge 0}$ be the distance function on $M$ defined as:
- $\forall A, B \in \CC: \map \d {A, B} :=$ the smallest $r \in \R_{\ge 0}$ such that $A$ and $B$ are each contained within the $r$-neighborhood of the other.
Then $\d$ is known as the Hausdorff metric on $M$.
Also known as
The Hausdorff metric is also known as the Hausdorff distance.
Also see
- Results about the Hausdorff metric can be found here.
Source of Name
This entry was named for Felix Hausdorff.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hausdorff metric