Flows in infinite networks represented by vector lattices Original Research Article

We are concerned with minimal cost flows in infinite networks. As an application of a Hahn-Banach type monotone extension theorem for convex cones, an abstract theorem characterizing minimal cost flows by local price systems is obtained for a general vector lattice situation. This result extends the usual finite network result, or rather its extension to some L1 – L∞ situation, which states that the minimal transportation cost is the supremum (taken over all local price systems) of the difference between consumption cost and transportation profit.