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EXTENSION OF THE BAUER'S MAXIMUM PRINCIPLE FOR COMPACT METRIZABLE SETS

Mohammed Bachir 1 
1 Equations d'evolution
SAMM - SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
Abstract : Let X be a nonempty convex compact subset of some Haus-dorff locally convex topological vector space S. The well know Bauer's maximum principle stats that every convex upper semi-continuous function from X into R attains its maximum at some extremal point of X. We give some extensions of this result when X is assumed to be compact metrizable. We prove that the set of all convex upper semi-continuous functions attaining there maximum at exactly one extremal point of X is a G δ dense subset of the space of all convex upper semi-continuous functions equipped with a metric compatible with the uniform convergence .
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Submitted on : Monday, December 17, 2018 - 2:09:29 AM
Last modification on : Friday, May 6, 2022 - 4:50:07 PM
Long-term archiving on: : Monday, March 18, 2019 - 12:50:42 PM

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  • HAL Id : hal-01956983, version 1
  • ARXIV : 1812.07243

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Mohammed Bachir. EXTENSION OF THE BAUER'S MAXIMUM PRINCIPLE FOR COMPACT METRIZABLE SETS. 2018. ⟨hal-01956983⟩

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