On equilibrium allocations as distributions on the commodity space

It is shown that the distribution of agents' characteristics is a concise and accurate description of an economy as far as Walrasian equilibrium analysis for large economies is concerned: Let E be an exchange economy; W(E), the set of Walras allocations for E; and DW(E), the set of distributions on the commodity space of the allocations in W(E). It is shown that for two atomless economies E₁ and E₂ which have the same distribution of agents' characteristics, the sets DW(E₁) and DW(E₂) have the same closure. For every distribution μ of agents' characteristics is defined a standard representation E^μ, and it is shown that DW(E^μ) is closed. Further, the correspondence μ {mapping}DW(E^μ) is shown to be upper hemicontinuous.