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A unifying approach to integration for bounded positive charges

de Cooman, Gert; Troffaes, Matthias; Miranda, Enrique

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Authors

Gert de Cooman

Enrique Miranda



Abstract

This paper deals with n-monotone functionals, which constitute a generalisation of n-monotone set functions. Using the notion of exactness of a functional, we introduce a new notion of lower and upper integral which subsumes as particular cases most of the approaches to integration in the literature. As a consequence, we can characterise which types of integrals can be used to calculate the natural extension (the lower envelope of all linear extensions) of a positive bounded charge.

Citation

de Cooman, G., Troffaes, M., & Miranda, E. (2008). A unifying approach to integration for bounded positive charges. Journal of Mathematical Analysis and Applications, 340(2), 982-999. https://doi.org/10.1016/j.jmaa.2007.09.026

Journal Article Type Article
Publication Date Apr 1, 2008
Deposit Date Jan 15, 2015
Publicly Available Date Mar 29, 2024
Journal Journal of Mathematical Analysis and Applications
Print ISSN 0022-247X
Electronic ISSN 1096-0813
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 340
Issue 2
Pages 982-999
DOI https://doi.org/10.1016/j.jmaa.2007.09.026
Keywords n-Monotonicity, Coherent lower prevision, Exact functional, Natural extension, Choquet integral, Comonotone additivity, Lower integral

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