On a set-valued integral

We have introduced in [5] an integral for multifunctions with respect to a multimeasure, both the multifunction and the multimeasure are taking values in the family of all nonempty compact convex subsets of a real Banach algebra. In this work we establish some relations between the integral defined in [5] and the integrals of Aumann [1], Brink – Maritz [3], Brooks [4] and Martellotti – Sambucini [9]. Then we give a Fichtenholz – Kantorovic type theorem using the integral defined in [5].