Krein-Milman theorem


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Krein-Milman theorem

[′krīn ′mil·mən ‚thir·əm]
(mathematics)
The theorem that in a locally convex topological vector space, any compact convex set K is identical with the intersection of all convex sets containing the extreme points of K.
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e](f) = [absolute value of e(f)]; then using the Krein-Milman theorem, it is easy to see that [tau] is separated.
The collection concludes with papers on the theory of complex functions, a proof of the Krein-Milman Theorem, and a review of the influence of Wedderburn on modern algebra.
The proof of this relies on a Krein-Milman theorem for Markov operators obtained in Section 2, a result of Goodearl, [6], stating that S is the inverse limit of a sequence of finite dimensional simplices, and the idea used in Example 2.
By the Hahn-Banach and the Krein-Milman Theorems, E(x) [not equal to] [empty set].