n-Monotone exact functionals

Details n-Monotone exact functionals n-Monotone exact functionals

2008-01-13

arxiv.org/abs/0801.1962v1

Mathematics

Functional Analysis

Scientific paper

10.1016/j.jmaa.2008.05.071

We study n-monotone functionals, which constitute a generalisation of n-monotone set functions. We investigate their relation to the concepts of exactness and natural extension, which generalise the notions of coherence and natural extension in the behavioural theory of imprecise probabilities. We improve upon a number of results in the literature, and prove among other things a representation result for exact n-monotone functionals in terms of Choquet integrals.

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