Measurable multifunctions and their applications to convex integral functionals

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.