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 .
|||W. Blaschke, "Kreis und Kugel" , Chelsea, reprint (1949)|
|[a1]||P.J. Kelly, M.L. Weiss, "Geometry and convexity" , Wiley (1979)|
Blaschke selection theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Blaschke_selection_theorem&oldid=32063