Blaschke selection theorem

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

Source: Wikipedia — Blaschke selection theorem (CC BY-SA 4.0)

Blaschke selection theorem

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

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Source: Wikipedia "Blaschke selection theorem" · CC BY-SA 4.0

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