A representation theorem for Aumann integrals (Q796677)

In this paper we establish some properties for Aumann integrals of set- valued functions \(F:T\to 2^ K\) whose values are non-empty subsets of a real separable reflexive Banach space X. Then, we give a representation theorem for the Aumann integral of set-valued functions of Souslin type which includes and extends some earlier results to the infinite dimensional case. Finally we prove a Lebesgue's Dominated Convergence theorem by using a convergence which seems rather natural in the infinite dimensional case. This last theorem, even in the finite dimensional case, strictly contains the well-known analogous result of Aumann which was given by means of the Kuratowski convergence.