Blaschke selection theorem

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Blaschke compactness principle

A metric space of convex bodies is locally compact, i.e. it is possible to select, out of an infinite set of convex bodies belonging to a given cube, a sequence which converges to some convex body in this cube.

The theorem was demonstrated in 1916 by W. Blaschke [1].


[1] W. Blaschke, "Kreis und Kugel" , Chelsea, reprint (1949)



[a1] P.J. Kelly, M.L. Weiss, "Geometry and convexity" , Wiley (1979)
How to Cite This Entry:
Blaschke selection theorem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article