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Integral Representation of Continuous Comonotonically Additive Functionals

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  • ZHOU, Lin

    (Cowles foundation, Yale University and CORE, Université catholique de Louvain)

Abstract

In this paper, I first prove an integral representation theorem: Every quasi-integralon a Stone lattice can be represented by a unique upper-continuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a compact space, and to prove the existence of an upper-continuous capacity on the product space of infinitely many compact Hausdorff spaces with a collection of consistent finite marginals.

Suggested Citation

  • ZHOU, Lin, 1996. "Integral Representation of Continuous Comonotonically Additive Functionals," LIDAM Discussion Papers CORE 1996005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1996005
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1996.html
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    Citations

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    Cited by:

    1. Roman Kozhan, 2011. "Non-additive anonymous games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 215-230, May.
    2. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2012. "Choquet Integration on Riesz Spaces and Dual Comonotonicity," Working Papers 433, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    3. Roman Kozhan & Michael Zarichnyi, 2008. "Nash equilibria for games in capacities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(2), pages 321-331, May.

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