Integral representation of continuous comonotonically additive functionals

DOI10.1090/S0002-9947-98-01735-8zbMath0905.28006MaRDI QIDQ4382983

Lin Zhou

Publication date: 24 March 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

weak topologycomonotonically additive functionalsKolmogorov's theoremStone latticescontinuous functionalsChoquet integralsquasi integralmonotonic functionalsconsistent marginalsregular capacitiesupper-continuous capacities

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Set functions and measures on topological spaces (regularity of measures, etc.) (28C15) Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures (28C05)

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Choquet integration on Riesz spaces and dual comonotonicity ⋮ Foundations of neo-Bayesian statistics ⋮ Attractive fixed-point solution study of shell model for homogeneous isotropic turbulence ⋮ Fractal dimensions for inclusion hyperspaces and non-additive measures ⋮ Strong solutions to stochastic hydrodynamical systems with multiplicative noise of jump type ⋮ Integral representation of belief measures on compact spaces ⋮ Shell model of turbulence perturbed by Lévy noise ⋮ Balanced capacities ⋮ A nonlinear extension of Korovkin's theorem ⋮ Signed integral representations of comonotonic additive functionals ⋮ Idempotent convexity and algebras for the capacity monad and its submonads ⋮ Nash equilibria for games in capacities ⋮ Non-additive anonymous games ⋮ Convex hyperspaces of probability measures and extensors in the asymptotic category ⋮ Choquet operators associated to vector capacities ⋮ A note on the Choquet type operators ⋮ Irreducibility and exponential mixing of some stochastic hydrodynamical systems driven by pure jump noise ⋮ Nonlinear functionals on \(C(X)\) and Choquet integrals ⋮ Limit laws for non-additive probabilities and their frequentist interpretation ⋮ Nonadditive measures and nonlinear integrals —focusing on a theoretical aspect— ⋮ LAWS OF LARGE NUMBERS FOR CONTINUOUS BELIEF MEASURES ON COMPACT SPACES ⋮ Subjective probability theory with continuous acts

Cites Work

• Non-additive measure and integral
• Theory of capacities
• Integral Representation Without Additivity
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