$H_\delta $-Embeddings in Hilbert Space and Optimization on $G_\delta $-Sets

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· American Mathematical Society: Memoirs of the American Mathematical Society Book 349 · American Mathematical Soc.
Ebook
101
Pages
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About this ebook

If [italic]K is a metrizable convex compact subset of a locally convex topological vector space, then all the following theorems hold for [italic]K: the Krein-Milman theorem on the extreme points of [italic]K; the Choquet integral representation theorem; the Bauer theorem on minimum points of concave lower semicontinuous functions on [italic]K. Roughly speaking, this memoir is devoted to extensions of these theorems to sets that are not compact and/or not convex.

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