An extension of Prohorov's theorem for transition probabilities with applications to infinite-dimensional lower closure problems (Q1084738)

The paper deals with results concerning the relative weak compactness property of sets of transition probabilities on \(T\times B(S)\), T being a space equipped with a fixed measure and B(S) denoting the \(\sigma\)- algebra of a standard Borel space S. The lower closure and lower semicontinuity theorems play a prominent role in the existence theory for optimal control and have been studied by many authors. The given result generalizes the previous one of the author [SIAM J. Control Optimization 22, 570-598 (1984; Zbl 0549.49005)] and can particularly be of use in obtaining existence theorems for the optimal control of distributed parameter systems.