# 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^{}.

## References

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

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 |