Representation of weak limits and definition of nonconservative products

The goal of this article is to show that the notion of generalized graphs i s able to represent the limit points of the sequence {g(u(n))du(n)} in the weak-star topology of measures when {u(n)} is a sequence of continuous func tions of uniformly bounded variation. The representation theorem induces a natural definition for the nonconservative product g(u)du in a BV context. Several existing definitions of nonconservative products are then compared, and the theory is applied to provide a notion of solutions and an existenc e theory to the Riemann problem for quasi-linear, strictly hyperbolic syste ms.