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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].

References

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


Comments

References

[a1] P.J. Kelly, M.L. Weiss, "Geometry and convexity" , Wiley (1979)
How to Cite This Entry:
Blaschke selection theorem. A.B. Ivanov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Blaschke_selection_theorem&oldid=12823
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098