Representation of increasing convex functionals with countably additive measures

2015/02/20 by Patrick Cheridito, Cheridito, Patrick, Michael Kupper +3
Mathematics · #28C05 #28C15 #47H07 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:28C05 #msc:28C15 #msc:47H07

paper · pdf · doi:10.48550/arxiv.1502.05763

arxiv created 2021/03/27 · arxiv updated 2021/03/30

Abstract

We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a sup-representation of functionals defined on spaces of real-valued Borel measurable functions. Our assumptions consist of sequential semicontinuity conditions which are easy to verify in different applications.

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