## You are here

HomeKrein-Milman theorem

## Primary tabs

# 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

Type of Math Object:

Theorem

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

46A03*no label found*52A07

*no label found*52A99

*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff