On Geometric Form of a Hahn–Banach Theorem’s Version for Idempotent Probability Measures

Abstract

In the present paper is showed that the idempotent semiring $$\overline{\mathbb{R}}_{\textrm{max}}$$ is reflexive. Further, is showed that the set $$I(X)$$ of idempotent probability measures is a subset of the complete semimodule $$\mathbb{R}_{\textrm{max}}^{\mathfrak{m}}$$ , but it is not a subsemimodule. Finally, it is established the Projector formula, the Universal separation theorem and the Hahn–Banach theorem for the idempotent subset $$I(X)\subset\overline{\mathbb{R}}^{\mathfrak{m}}_{\textrm{max}}$$ on the predual pair $$(\overline{\mathbb{R}}_{\textrm{max}},\,\overline{\mathbb{R}}^{\mathfrak{m}}_{\textrm{max}})$$ over the idempotent semiring $$\overline{\mathbb{R}}_{\textrm{max}}$$ , although $$I(X)$$ is not a subsemimodule.

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DOI

10.1134/s1995080223110367

Citations and references