L'intégration par rapport à une mesure de Radon vectorielle

Summary:Let $X$ be a quasicomplete locally convex Hausdorff space. Let $T$ be a locally compact Hausdorff space and let $C_0(T) = lbrace f: T ightarrow I$, $f$ is continuous and vanishes at infinity$ brace $ be endowed with the supremum norm. Starting with the Borel extension theorem for $X$-valued $sigma $-additive Baire measures on $T$, an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map $u: C_0(T) ightarrow X$ to be weakly compact