Sur la compacité des multimesures (I)

Let $\text{M}{}_{\mathrm{+}}\text{(T,}\text{K}\text{,}\text{ck}\text{(E))}$ be the space of positive $\text{K}$-regular set-valued measures defined on a σ-algebra $\text{B}$ with values in the space of all compact non empty convex subsets of a Banach space E. We characterize the compact subsets of $\text{M}{}_{\mathrm{+}}\text{(T,}\text{K}\text{,}\text{ck}\text{(E))}$ endowed with the weakest topology for which all mappings M→M(A), $\text{A∈}\text{B}$ are continuous. The case of real nonnegative measures has been investigated by Topsøe 6], Grothendieck 3] and others. To cite this article: K.K. Siggini, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 949–952.