pages/more-functional-analysis/locally-convex-spaces/krein-milman-theorem.md


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---
title: Krein–Milman Theorem
parent: Locally Convex Spaces
grand_parent: More Functional Analysis
nav_order: 2
---

# {{ page.title }}

## Extreme Points

{% definition Extreme Point %}
Suppose $C$ is a convex subset of a vector space $X$.
We say that an element $x \in C$ is an *extreme point* of $C$
if
{% enddefinition %}

{% proof %}
{% endproof %}