International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 1, Pages 175-191
Measurable multifunctions and their applications to convex integral functionals
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.