A representation theorem for maxitive measures

Egoroff Theorem for Operator-Valued Measures in Locally Convex Cones

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

On the Basic Representation Theorem for Convex Domination of Measures

A direct, constructive proof is given for the basic representation theorem for convex domination of measures. The proof is given in the finitistic case Žpurely . atomic measures with a finite number of atoms , and a simple argument is then given to extend this result to the general case, including both probability measures and finite Borel measures on infinite-dimensional spaces. The infinite-d...

Risk Aversion and Coherent Risk Measures: a Spectral Representation Theorem

We study a space of coherent risk measures Mφ obtained as certain expansions of coherent elementary basis measures. In this space, the concept of “Risk Aversion Function” φ naturally arises as the spectral representation of each risk measure in a space of functions of confidence level probabilities. We give necessary and sufficient conditions on φ for Mφ to be a coherent measure. We find in thi...

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

Open Mappings of Probability Measures and the Skorohod Representation Theorem

We prove that for a broad class of spaces X and Y (including all Souslin spaces), every open surjective mapping f : X ! Y induces the open mapping 7 ! f ?1 between the spaces of probability measures P(X) and P(Y). Connections with the Skorohod representation theorem and its generalizations are discussed.