A unifying approach to integration for bounded positive charges

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

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: Jan 16, 2015
• 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
• Public URL: https://durham-repository.worktribe.com/output/1570474