Blaschke selection theorem

The Blaschke selection theorem is a result in topology and convex geometry about sequences of convex sets. Specifically, given a sequence ${\displaystyle \{K_{n}\}}$ of convex sets contained in a bounded set, the theorem guarantees the existence of a subsequence ${\displaystyle \{K_{n_{m}}\}}$ and a convex set ${\displaystyle K}$ such that ${\displaystyle K_{n_{m}}}$ converges to ${\displaystyle K}$ in the Hausdorff metric. The theorem is named for Wilhelm Blaschke.

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