Representation of increasing convex functionals with countably additive measures

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2021
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Studia Mathematica. Institute of Mathematics, Polish Academy of Sciences. 2021, 260, pp. 121-140. ISSN 0039-3223. eISSN 1730-6337. Available under: doi: 10.4064/sm181107-16-2
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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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ISO 690CHERIDITO, Patrick, Michael KUPPER, Ludovic TANGPI, 2021. Representation of increasing convex functionals with countably additive measures. In: Studia Mathematica. Institute of Mathematics, Polish Academy of Sciences. 2021, 260, pp. 121-140. ISSN 0039-3223. eISSN 1730-6337. Available under: doi: 10.4064/sm181107-16-2
BibTex
@article{Cheridito2021Repre-31211.2,
  year={2021},
  doi={10.4064/sm181107-16-2},
  title={Representation of increasing convex functionals with countably additive measures},
  volume={260},
  issn={0039-3223},
  journal={Studia Mathematica},
  pages={121--140},
  author={Cheridito, Patrick and Kupper, Michael and Tangpi, Ludovic}
}
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