Various developments in mathematical economics and optimal control have led to the study
of the measurability of multivalued mappings. Castaing, in his recent thesis [2](partly …

1. Introduction. Let (X, p) be a metric space, and let 2x denote the collection of nonempty
closed subsets of X. If (T, d) is a compact metric space, and if, u is a positive Radon measure …

Consider a measurable space (T,~), a complete separable metric space X and ra
multifunction from T to non empty closed subsets of X. An important problem is the existence …

A set-valued measure is a $\sigma $-additive set-function which takes on values in the
nonempty subsets of a euclidean space. It is shown that a bounded and non-atomic set …

Introduction. The union of an open ball in IRa with any non measurable subset of its
boundary provides an example of a non Borel convex set. It is a less immediate observation …

Set-valued measures whose values are subsets of a Banach space are studied. Some basic
properties of these set-valued measures are given. Radon-Nikodym theorems for set-valued …

If (x)=~ f (s, x (s)) p (ds), x EX, where X is a linear space of measurable functions defined on
a measure space(S, A,~) and having values in a linear space E. The function f: S x E § R is …

By a set function we shall here mean a non-negative, possibly infinitevalued function
defined on a paving. Let fi be a set function defined on the paving../.. In all the definitions …

The question of uniqueness of representing measures is a natural one, both in applications
and in the theory itself. As always, one must specify clearly the context within which …

Let (SŽ, X) be a measurable space, X a real Banach space and v: SŽ–> X a countably
additive vector measure.. We define a X-measurable function f: Q–> R to be weakly v …