Krein-Milman theorem
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Krein-Milman theorem
Theorem.
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.
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 General theory of locally convex spaces52A07 Convex sets in topological vector spaces
52A99 None of the above, but in MSC2010 section 52Axx
