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Department of Mathematical Sciences

Staff

Publication details for Dr Matthias Troffaes

de Cooman, Gert, Troffaes, Matthias & Miranda, Enrique (2008). A unifying approach to integration for bounded positive charges. Journal of Mathematical Analysis and Applications 340(2): 982-999.

Author(s) from Durham

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.