Representation of a max-plus-gauge of the set of idempotent probability measures by the guage of the set of probability measures

In the paper a max-plus-gauge of the set of idempotent probability measures represents by the guage of the set of probability measures. It is shown that every max-plus ball is max-plus convex. It is established that every max-plus linear functional on finite dimensional max-plus normed space is bounded. We obtain that every max-plus finite dimensional space and its max-plus dual space are isomorphic.

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