Approximation theory for generalized young measures

Young measures can be understood as certain linear continuous functionals on a space of Caratheodory integrands, which gives a basis for their various generalizations. The (generalized) Young measures can be approximated by several techniques classified here according to the shape (convex/nonconvex) and dimensionality (finite/infinite) of the resulting set of all (semi)discretized generalized Young measures. A general theory for convex approximations is developed here and illustrative applications to a relaxed optimization problem are given to compare various techniques.