Normal fields of functionals and optimal measurable sections (Q1359461)

Let \((A_t,t\in T;X)\) be a measurable field of metric spaces and \(f_t: A_t\to R\cup\{-\infty\}\) a family of functions. Define maximal reward as \(v(t):=\sup\{f_t(a): a\in A\}\). The main subject of the paper is the measurability of \(v\) and sufficient conditions for the existence of optimal masurable sections \(x^*\in X\) (=elements satisfying \(f_t(x^*(t))= v(t)\) for all \(t\in T\)). The results are applicable in decision theory.