Krein-Milman theorem

Theorem.

Let $X$ be a locally convex topological vector space, and let $K\\subset X$ 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.

References

1 H. L. Royden. . Prentice-Hall, Englewood Cliffs, New Jersey, 1988

单词	KreinMilmanTheorem
释义	Krein-Milman theorem Theorem. Let $X$ be a locally convex topological vector space, and let $K\\subset X$ 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. References 1 H. L. Royden. . Prentice-Hall, Englewood Cliffs, New Jersey, 1988
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