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Economies in InfiniteDimensional Spaces
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aggregate production set assume belongs Bewley's Borel measures bounded sequence boundedness budget constraint bundle ca(T closed convex commodity space compact set compactness assumptions consumer consumption and production continuous continuous linear functional converges convex cone convex hull convex sets dual lattice dual space duction economy in L efficiency of production equilibrium exists equilibrium price equivalence classes example existence of equilibria existence theorem extremely desirable commodities feasible allocation feasible consumption sets feasible production sets find vectors finite-dimensional Gateaux derivative guarantee Hahn-Banach Theorem Hausdorff vector space Hence However implies infinite-dimensional initial endowment input interiority assumptions J-compact K s t Lebesgue space limit price linear functional local nonsatiation marginal efficiency marginal rates marginal utility Mas-Colell measure space metric space models monotone monotone function monotone preferences nonempty norm bounded norm interior norm topology normed lattice normed space noted open set open subset order intervals output Pareto optimal positive cone positive elements preference relation principal order ideal production is strongly production is weakly production plans production possibility set profit-maximization proof of Theorem quasi-equilibrium real number reflexive space relatively returns to scale Riesz Decomposition Property satisfies second firm Section separating hyperplane theorem sequence set of feasible set X set Y sets are norm sigma-finite measure Since space L Standard Assumptions strictly positive strongly bounded subeconomies subset of L subspace sumer supporting hyperplanes topology on L upper semicontinuous utility function vector space topology vectors x weak topology weak-star compact weak-star topology weakly bounded weakly compact x+Xv Zame zero functional