Habib Benfriha
University of Oran1, Oran, Algeria

In this paper we introduce a convergence notion on the set bv(I) of all functions with bounded variation on $[a,b]$ or $(a,b)$; $I=[a,b]$ or $I=(a,b)$. We show that the weak convergence of a sequence of positive measures on $I$ is equivalent with the new type of convergence on the set $bv(I)$ of the repartition on the measures. We use the direct and inverse convergence theorem of Helly and Bray. The compactness phenomena is also studied.