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We present a result on convexity and weak compactness of the range of a vector measure with values in a Banach space, based on the Maharam classification of measure spaces. Our result extends a recent result of Khan and Sagara (Illinois J. Math. 2013). We apply our result to integration of Banach space valued correspondences and to the core-Walras equivalence problem in coalitional exchange economies with an infinite-dimensional commodity space.

Liapounoff’s vector measure theorem in Banach spaces and applications to general equilibrium theory