Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Choquet integration on Riesz spaces and dual comonotonicity


Authors: Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci and Luigi Montrucchio
Journal: Trans. Amer. Math. Soc. 367 (2015), 8521-8542
MSC (2010): Primary 28A12, 28A25, 28C05, 46B40, 46B42, 46G12
DOI: https://doi.org/10.1090/tran/6313
Published electronically: May 13, 2015
MathSciNet review: 3403064
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 28A12, 28A25, 28C05, 46B40, 46B42, 46G12

Retrieve articles in all journals with MSC (2010): 28A12, 28A25, 28C05, 46B40, 46B42, 46G12


Additional Information

Simone Cerreia-Vioglio
Affiliation: Dipartimento di Scienze delle Decisioni and IGIER, Università Bocconi, via Sarfatti, 25 Milan, Italy

Fabio Maccheroni
Affiliation: Dipartimento di Scienze delle Decisioni and IGIER, Università Bocconi, via Sarfatti, 25 Milan, Italy

Massimo Marinacci
Affiliation: Dipartimento di Scienze delle Decisioni and IGIER, Università Bocconi, via Sarfatti, 25 Milan, Italy

Luigi Montrucchio
Affiliation: Collegio Carlo Alberto, Università di Torino, via Real Collegio 30, 10024 Moncalieri Torino, Italy

DOI: https://doi.org/10.1090/tran/6313
Received by editor(s): April 27, 2012
Received by editor(s) in revised form: September 29, 2013
Published electronically: May 13, 2015
Additional Notes: The financial support of ERC (Advanced Grant BRSCDP-TEA), AXA Research Fund, and MIUR (Grant PRIN 20103S5RN3_005) is gratefully acknowledged
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society