Infinite networks: Minimal cost flows Original Research Article

We are concerned with the minimal cost flow problem in infinite networks. The generalisation to infinite networks is made in order to provide tools for the study of the dynamics of such networks. By disintegration methods, we obtain that the minimal transportation costs are the supremum of the differences between consumption cost and transportation profit taken over all local price systems. Thus, by our method, results for which finite networks are usually obtained by the strong duality theorem, can be generalized to infinite networks.