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arXiv · 1812.07243

Extension Of The Bauer's Maximum Principle For Compact Metrizable Sets

Mohammed Bachir
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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 $\delta$ 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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Mohammed Bachir. 2018-12-18. Extension Of The Bauer's Maximum Principle For Compact Metrizable Sets. https://arxiv.org/abs/1812.07243

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