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Blaschke selection theorem : ウィキペディア英語版
Blaschke selection theorem
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 K such that K_ converges to K in the Hausdorff metric. The theorem is named for Wilhelm Blaschke.
==Alternate statements==

* A succinct statement of the theorem is that a metric space of convex bodies is locally compact.
* Using the Hausdorff metric on sets, every infinite collection of compact subsets of the unit ball has a limit point (and that limit point is itself a compact set).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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