The finitely additive integral of multifunctions with closed and convex values

We investigate integation with respect to a finitely additive measure for an integrand with closed and convex values in aseparable and reflexive Banach space, and we obtain a closedness result for the Aumann integral. To this aim we first define scalarly the Stone extensions for the selections, using the identification of the target space with its bidual, and then define the integral via selection. Finally, with the use of Radstrom’s Embedding Theorem and the identification of the Aumann and the Debreu integral for the Stone extension we achieve the closedness and the convexity of the Aumann integral.