Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 3, 409--427

Random Correspondences as Bundles of Random Variables

By

Adriana Castaldo, University of Sussex, Brighton, U.K.
Fabio Maccheroni, Universit{\'a} Bocconi, Milano, Italy
Massimo Marinacci, Universit{\'a} di Torino, Torino, Italy

SUMMARY. We relate the distributions induced by random sets with the distributions induced by their measurable selections, thus providing a probabilistic foundation for viewing random sets as ``sets'' of random variables. In so doing we revisit and extend some results of Artstein, Hart, Hess, and Kohlberg, and we obtain a ``change of variable formula'' for the Aumann integral of a random set.

AMS (1991) subject classification}. 28B20, 28A12, 54C60, 54C65, 60D05.

Key words and phrases. Distributions of random sets, measurable selections, Choquet integral, Aumann integral.

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