On approximate decentralization of Pareto optimal allocations in locally convex spaces
Extending the second fundamental theorem of welfare economics to economies with a topological vector space of commodities \textit{G. Debreu} [Proc. Nat. Acad. Sci. USA 40, 588-592 (1954; Zbl 0055.380)], supposed that the aggregate production set is a convex set with nonempty interior and applied then the supporting hyperplane theorem. The authors extend this result, renouncing the interiority assumption and replacing it by some weak closure (Choquet condition), local compactness (Dieudonné condition) and order conditions. The main idea of the paper is to find an approximate support (\(\epsilon\)-support) to the closure of a convex set with empty interior which enables the authors to find an approximate version of the Debreu result (an exact result is also included). The paper uses in an essential way recent results in functional analysis obtained by G. Choquet, J. Dieudonné, Ky Fan, E. Bishop and R. R. Phelps.
scientific article; zbMATH DE number 4053301
scientific article