Hölder inequality on the space of upper semicontinuous functions

Abstract

For a compact Hausdorff space X, we consider the space IB(X) of all idempotent probability measures on X, which are defined as set-functions on the σ-algebra of all Borel subsets of X, and also the space IUSC(X) of all normalized max-plus linear functionals on the linear space of all upper semicontinuous functions on X, equipped with idempotent operations. In the main result it is established that a max-plus version of the Hölder inequality holds on the space of upper semicontinuous functions.