# Blaschke selection theorem

From Encyclopedia of Mathematics

*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