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Difference between revisions of "Blaschke selection theorem"

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''Blaschke compactness principle''
 
''Blaschke compactness principle''
  

Latest revision as of 15:21, 1 May 2014

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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Blaschke_selection_theorem&oldid=12823
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article