Abstract

Two generalizations of Komlós’ theorem for functions and multifunctions with values in a Banach space are presented. The first generalization is partly new and the second one is a Komlós-type result of a completely new nature. It requires the Radon-Nikodym property for the Banach space and its dual. In both cases our approach relies on using Komlós’ theorem by means of a diagonal extraction argument, as introduced in [5], [6], [7]. Two quite general lower closure-type results, which follow immediately from our main results, are shown to generalize or substantially extend a number of results in the literature.

Author information

Contact details are reproduced from the original publication and may be historical.

Erik J. Balder

Mathematical Institute, University of Utrecht, 3508 TA Utrecht, the Netherlands.

Christian Hess

Ceremade, URA CNRS No. 749, Université Paris Dauphine 75775 Paris Cedex 16, France.

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Suggested citation

E. J. Balder, C. Hess. “Two Generalizations of Komlós' Theorem with Lower Closure-Type Applications.” Journal of Convex Analysis 3 (1996), No. 1, 25–44. https://doi.org/10.68381/jca03002

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Published by Heldermann Verlag, 1996. Rights now held by Banach Press.