Choquet integration on Riesz spaces and dual comonotonicity

Cerreia-Vioglio, Simone; Maccheroni, Fabio; Marinacci, Massimo; Montrucchio, Luigi

doi:10.1090/tran/6313

Choquet integration on Riesz spaces and dual comonotonicity
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by Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci and Luigi Montrucchio PDF

Trans. Amer. Math. Soc. 367 (2015), 8521-8542 Request permission

Abstract:

We give a general integral representation theorem for nonadditive functionals defined on an Archimedean Riesz space $X$ with unit. Additivity is replaced by a weak form of modularity, or, equivalently, dual comonotonic additivity, and integrals are Choquet integrals. Those integrals are defined through the Kakutani isometric identification of $X$ with a $C\left (K\right )$ space. We further show that our 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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