Choquet Integration on Riesz Spaces and Dual Comonotonicity
We give a general integral representation theorem (Theorem 6) for nonadditive functionals de?ned on an Archimedean Riesz space X with order unit. Additivity is replaced by a weak form of modularity, or equivalently dual comonotonic additivity, and integrals are Choquet integrals. Those integrals are de?ned through the Kakutani  isometric identi?cation of X with a C (K) space. We further show that our novel notion of dual comonotonicity naturally generalizes and characterizes the notions of comonotonicity found in the literature when X is assumed to be a space of functions.
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- ZHOU, Lin, 1996. "Integral Representation of Continuous Comonotonically Additive Functionals," CORE Discussion Papers 1996005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2010. "Singed Integral Representations of Comonotonic Additive Functionals," Working Papers 366, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
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