In this short paper we prove the equivalence between the RadonNikodym Theorem for reflexive Banach spaces and the representability of weakly compact operators with domain L(μ).

Let X be a Banach space and (Ω,Σ, λ) be a finite measure space, 1 ≤ p < ∞. It is shown that L(λ,X) has the Near Radon-Nikodym property if and only if X has it. Similarly if E is a Köthe function space that does not contain a copy of c0, then E(X) has the Near Radon-Nikodym property if and only if X does.

Idempotent integration is an analogue of the Lebesgue integration where σ-additive measures are replaced by σ-maxitive measures. It has proved useful in many areas of mathematics such as fuzzy set theory, optimization, idempotent analysis, large deviation theory, or extreme value theory. Existence of Radon–Nikodym derivatives, which turns out to be crucial in all of these applications, was prov...

In this paper we clarify the relation between inverse systems, the Radon-Nikodym property, the Asymptotic Norming Property of James-Ho [JH81], and the GFDA spaces introduced in [CK06].

The Radon-Nikodym theorems of Segal and Zaanen are principally concerned with the classification of those measures p. for which any X« p. is given in the form

We show that computability of the Radon-Nikodym derivative of a measure μ absolutely continuous w.r.t. some other measure λ can be reduced to a single application of the non-computable operator EC, which transforms enumeration of sets (in N) to their characteristic functions. We also give a condition on the two measures (in terms of the computability of the norm of a certain linear operator inv...