The notion of max-min measure is a counterpart of the notion of maxplus measure (Maslov measure or idempotent measure). In this paper we consider the spaces of max-min measures on the compact Hausdorff spaces. It is proved that the obtained functor of max-min measures is isomorphic to the functor of max-plus (idempotent) measures considered by the second-named author. However, it turns out that the monads generated by these functors are not isomorphic.2010 Mathematics Subject Classification. 28A33, 46E27. Key words and phrases. Max-min measure, max-plus measure, compact Hausdorff space, monad. The authors are indebted to the referees for their important remarks.
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