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A unifying approach to integration for bounded positive charges |
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| Authors: | Gert de Cooman Matthias CM Troffaes Enrique Miranda |
| Institution: | aGhent University, SYSTeMS Research Group, Technologiepark, Zwijnaarde 914, 9052 Zwijnaarde, Belgium;bDurham University, Department of Mathematical Sciences, Science Laboratories, South Road, Durham, DH1 3LE, England, UK;cRey Juan Carlos University, Department of Statistics and Operations Research, C-Tulipán s/n, 28933 Móstoles, Spain |
| 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. |
| Keywords: | n-Monotonicity Coherent lower prevision Exact functional Natural extension Choquet integral Comonotone additivity Lower integral |
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