Krein-Milman theorem


Let X be a locally convex topological vector space, and let KX be a compact convex subset ( Then K is the closed convex hullMathworldPlanetmath of its extreme pointsPlanetmathPlanetmath.

The closed convex hull above is defined as the intersection of all closed convex subsets of X that contain K. This turns out to be the same as the closure of the convex hull in a topological vector spaceMathworldPlanetmath.


  • 1 H. L. Royden. . Prentice-Hall, Englewood Cliffs, New Jersey, 1988
Title Krein-Milman theorem
Canonical name KreinMilmanTheorem
Date of creation 2013-03-22 14:24:58
Last modified on 2013-03-22 14:24:58
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 6
Author jirka (4157)
Entry type Theorem
Classification msc 46A03
Classification msc 52A07
Classification msc 52A99