Krein-Milman theorem

Theorem.

Let $X$ be a locally convex topological vector space, and let $K\mathrm{\subset }X$ be a compact convex subset (http://planetmath.org/ConvexSet). Then $K$ is the closed convex hull of its extreme points.

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 space.

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