Theorem 1   Let be a locally convex topological vector space, and let be a compact convex subset. Then 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 that contain . This turns out to be the same as the closure of the convex hull in a topological vector space.

Bibliography

1

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