Semicontinuous integrands as jointly measurable maps - Oriol Carbonell-Nicolau (Rutgers University, Department of Economics, 2015)
Suppose that (X,A) is a measurable space and Y is a metrizable, Souslin space. Let Au denote the universal completion of A. Given f : X x Y !R and x 2 X, let f (x,xc) be the lower semicontinuous hull of f (x,xc). If f is (Au B(Y),B(R))-measurable, then f is (Au B(Y),B(R))-measurable.
Keywords: C30; A20; 330; lower semicontinuous hull; jointly measurable function; measurable projection; theorem; normal integrand