Integral Representation of Continuous Comonotonically Additive Functionals
AbstractIn 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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Bibliographic InfoPaper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1996005.
Date of creation: 01 Mar 1996
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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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- Roman Kozhan, 2011. "Non-additive anonymous games," International Journal of Game Theory, Springer, vol. 40(2), pages 215-230, May.
- 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.
- Roman Kozhan & Michael Zarichnyi, 2008. "Nash equilibria for games in capacities," Economic Theory, Springer, vol. 35(2), pages 321-331, May.
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