Equally Distributed Correspondences

Sergiu Hart and Elon Kohlberg

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The distribution of a correspondence φ is defined, and its connection with the set DLφ of distributions of its integrable selections is explored. The main result is that if φ1 and φ2 are equally distributed, i.e., if 1 = 2 , then DLφ1 and DLφ2 have the same closure in the weak convergence topology.