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# Krein-Milman theorem

###### Theorem.

Let $X$ be a locally convex topological vector space, and let $K\subset X$ be a compact convex subset. 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.
*Real Analysis*. Prentice-Hall, Englewood Cliffs, New Jersey, 1988

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Theorem

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## Mathematics Subject Classification

46A03*no label found*52A07

*no label found*52A99

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