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Equally Distributed Correspondences

Sergiu Hart and Elon Kohlberg

**Abstract**

The distribution *Dφ*
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
*φ*_{1} and
*φ*_{2} are equally distributed, i.e., if
*Dφ*_{1} =
*Dφ*_{2} ,
then
*DLφ*_{1} and
*DLφ*_{2}
have the same closure in the weak convergence topology.

*Journal of Mathematical Economics* 1 (1974), 2, 167-174