International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 1, Pages 175-191

Measurable multifunctions and their applications to convex integral functionals

Nikolaos S. Papageorgiou

University of California, 1015 Department of Mathematics, Davis 95616, California, USA

Received 6 June 1988; Revised 26 September 1988

Copyright © 1989 Nikolaos S. Papageorgiou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The purpose of this paper is to establish some new properties of set valued measurable functions and of their sets of Integrable selectors and to use them to study convex integral functionals defined on Lebesgue-Bochner spaces. In this process we also obtain a characterization of separable dual Banach spaces using multifunctions and we present some generalizations of the classical “bang-bang” principle to infinite dimensional linear control systems with time dependent control constraints.