Abstract
The starting point of this paper is a theorem of König concerning the distribution of given quantities of finitely many commodities among a finite number of consumers, each of them having a certain total demand to be satisfied within some individual subset of the commodity set; see [l2; p.24] and [11, p.139]. Problems of this type naturally arise from capacity models and are usually treated with the methods of discrete mathematics. One may apply, for instance, the theory of flows in finite networks in the sense of Ford-Fulkerson [1] to this and related problems. In his lectures on mathematical economics [12], König gave a completely different approach based on suitable versions of the Hahn-Banach theorem. Later on this method was elaborated and extended by Fuchssteiner in a series of papers [2], [3], [4], [6]. The final stage of his theory is included in the monograph on convex cones [5] and culminates in a measure theoretic result on flows in abstract networks.
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Neumann, M.M. (1985). The Theorem of Gale for Infinite Networks and Applications. In: Anderson, E.J., Philpott, A.B. (eds) Infinite Programming. Lecture Notes in Economics and Mathematical Systems, vol 259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46564-2_12
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DOI: https://doi.org/10.1007/978-3-642-46564-2_12
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