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world:krein [2026/04/11 08:16] rdouc |
world:krein [2026/04/11 08:26] (current) rdouc ↷ Page name changed from world:choquet to world:krein |
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| - | ====== Krein-Milman, Choquet and Birkhoff-Von Neuman Theorems ====== | + | ====== Krein-Milman and Birkhoff-Von Neuman Theorems ====== |
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| - | **Theorem (Choquet).** Let $E$ be an Euclidean space and $K \subset E$ convex and compact. Let $f : E \to \mathbb{R}$ be linear. Then $f$ attains its minimum on $K$ at a point of $\mathrm{Extr}(K)$. | + | **Corollary.** Let $E$ be an Euclidean space and $K \subset E$ convex and compact. Let $f : E \to \mathbb{R}$ be linear. Then $f$ attains its minimum on $K$ at a point of $\mathrm{Extr}(K)$. |
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world/krein.1775888202.txt.gz · Last modified: 2026/04/11 08:16 by rdouc
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