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Representation of increasing convex functionals with countably additive measures

Volume 260 / 2021

Patrick Cheridito, Michael Kupper, Ludovic Tangpi Studia Mathematica 260 (2021), 121-140 MSC: Primary 47H07, 28C05, 28C15. DOI: 10.4064/sm181107-16-2 Published online: 1 April 2021

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.

Authors

  • Patrick CheriditoDepartment of Mathematics
    ETH Zurich
    8092 Zurich, Switzerland
    e-mail
  • Michael KupperDepartment of Mathematics
    University of Konstanz
    Konstanz, Germany
    e-mail
  • Ludovic TangpiDepartment of Operations Research and Financial Engineering
    Princeton University
    Princeton, NJ, U.S.A.
    e-mail

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