Suppose (T,M) is a measurable space, X is a topological space, and ∅≠F(t)⊂X for t∈T.
Denote GrF={(t,x):x∈F(t)\}. The problem surveyed (reviewing work of others) is that of …

In this paper we attempt a unification of several selection theorems in the literature by
introducing the notion of a selection class and give sufficient conditions for the existence of …

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 …

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 …

These notes build upon a course I taught at the University of Maryland during the fall of
1983. My great thanks go to Martino Bardi, who took careful notes, saved them all these …

In 1959 AF Filippov published a paper [l] containing a lemma designed for use in the study
of optimal control problems. Stated somewhat imprecisely, let k be a continuous function on …

This paper continues the study of continuous selections begun in (13; 14; 15) and the
expository paper (12). The purpose of these papers, which is described in detail in the …

The existence of admissible strategies γ(⋅,⋅) minimizing a function E\int_0^1c(t,x,γ(t,x))dt is
studied, with x=x(⋅,ω) a continuous stochastic process, and admissible strategies defined as …

We give a measurable selection theorem which generalizes von Neumann-Aumann's
theorem when the domain of definition is an abstract measurable space and the range …

Many control problems can be naturally formulated, analyzed, and solved in a set-theoretic
context. Sets appear naturally when three aspects, which are crucial in control systems …