Representation of increasing convex functionals with countably additive measures

Representation of increasing convex functionals with countably additive measures

We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of realvalued continuous functions and the second a sup-representation of functionals defined on spaces of real-valued measurable functions. MSC 2010: 47H07, 28C05, 28C15

Uniform measures and countably additive measures

Uniform measures are defined as the functionals on the space of bounded uniformly continuous functions that are continuous on bounded uniformly equicontinuous sets. If every cardinal has measure zero then every countably additive measure is a uniform measure. The functionals sequentially continuous on bounded uniformly equicontinuous sets are exactly uniform measures on the separable modificati...

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

Nonconglomerability for countably additive Measures that are not κ-additive

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti (1974) and Dubins (1975), subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­‐ additive has conditional probabilities that fail to be conglomerable i...

ADDITIVE FUNCTIONALS OF d-ARY INCREASING TREES

A tree functional is called additive if it satisfies a recursion of the form F (T ) = ∑k j=1 F (Bj)+f(T ), where B1, . . . , Bk are the branches of the tree T and f(T ) is a toll function. We prove a general central limit theorem for additive functionals of d-ary increasing trees under suitable assumptions on the toll function. The same method also applies to generalised planeoriented increasin...