Integral Representation of Continuous Comonotonically Additive Functionals

Lin Zhou

No 1996005, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper, I first prove an integral representation theorem: Every quasi-integralon a Stone lattice can be represented by a unique upper-continuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a compact space, and to prove the existence of an upper-continuous capacity on the product space of infinitely many compact Hausdorff spaces with a collection of consistent finite marginals.

Keywords: Upper-continuous capacities; regular capacities; Choquet integrals; Stone lattices; comonotonically additive functionals; monotonic functionals; continuous functionals; the weak topology; Kolmogorov's theorem; consistent marginals (search for similar items in EconPapers)
Date: 1996-03-01
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