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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)

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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.

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File URL: http://alfresco.uclouvain.be/alfresco/download/attach/workspace/SpacesStore/57bc2360-9237-42fb-8825-8321a670fa0d/coredp_1996_05.pdf
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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1996005.

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Date of creation: 01 Mar 1996
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Handle: RePEc:cor:louvco:1996005

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Related research

Keywords: Upper-continuous capacities; regular capacities; Choquet integrals; Stone lattices; comonotonically additive functionals; monotonic functionals; continuous functionals; the weak topology; Kolmogorov's theorem; consistent marginals;

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Cited by:
  1. Roman Kozhan & Michael Zarichnyi, 2008. "Nash equilibria for games in capacities," Economic Theory, Springer, vol. 35(2), pages 321-331, May.
  2. Roman Kozhan, 2008. "Non-Additive Anonymous Games," Working Papers wp08-04, Warwick Business School, Finance Group.
  3. 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.

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