# Blaschke selection theorem

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)