Blaschke_selection_theorem
Blaschke selection theorem
Any sequence of convex sets contained in a bounded set has a convergent subsequence
The Blaschke selection theorem is a result in topology and convex geometry about sequences of convex sets. Specifically, given a sequence of convex sets contained in a bounded set, the theorem guarantees the existence of a subsequence and a convex set such that converges to in the Hausdorff metric. The theorem is named for Wilhelm Blaschke.