Theorems on double large economies and on the integral of banach space valued correspondences

In this study we analyze Pareto optimal and core allocations of an exchange economy containing a Banach space of commodities and a measure space of traders. We show that in such an economy E, if a coalition C blocks an allocation, then a sufficiently small perturbation of C will also block the allocation. It is also shown that the Pareto set and the core of E are closed subsets of the Banach space of all integrable mappings of the consumer space into the commodity space. Provided that the commodity space of E is separable, we give a strengthening of this result by considering a particular form of convergence of a sequence of economies. To obtain these theorems on double large economies we establish several results related to the integral of B-space valued correspondences.