Open AccessChoquet integration on Riesz spaces and dual comonotonicity
Author(s) -
Simone CerreiaVioglio,
Fabio Maccheroni,
Mássimo Marinacci,
Luigi Montrucchio
Publication year - 2015
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/6313
Subject(s) - algorithm , type (biology) , annotation , artificial intelligence , mathematics , computer science , ecology , biology
We give a general integral representation theorem for nonadditive functionals defined on an Archimedean Riesz space X 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 X with a C ( K ) 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 X is assumed to be a space of functions.