Vector versions of a density theorem and applications to problems of control theory (Q789721)

The author studies extreme points of a convex set of measurable selections, defined by unilateral vector integral constraints. At first a vector version of the density theorem due \textit{C. Castaing} and \textit{M. Valadier} [Convex analysis and measurable multifunctions, Lect. Notes Math. 580 (1977; Zbl 0346.46038)] is established for such sets. Next, some applications to control problems with operator constraints are given. The main tools are the Krein-Milman theorem and the technique of measurable selections.