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A unifying approach to integration for bounded positive charges.

de Cooman, Gert and Troffaes, Matthias and Miranda, Enrique (2008) 'A unifying approach to integration for bounded positive charges.', Journal of mathematical analysis and applications., 340 (2). pp. 982-999.

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.

Item Type:Article
Keywords:n-Monotonicity, Coherent lower prevision, Exact functional, Natural extension, Choquet integral, Comonotone additivity, Lower integral
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1016/j.jmaa.2007.09.026
Record Created:15 Jan 2015 14:35
Last Modified:16 Jan 2015 12:12

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