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

In the present paper is showed that the idempotent semiring is reflexive. Further, is showed that the set of idempotent probability measures is a subset of the complete semimodule , 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 on the predual pair over the idempotent semiring , although is not a subsemimodule.