Projections on convex sets in the relaxed limit (Q5945285)

The aim of this paper is to study the continuity of the best approximation of an \(L^{p}\)-function, \(1\leq p<\infty,\) on closed convex sets, when they vary and converge to a limit set with an appropriate convergence concept. To this end three sections of the paper with independent interest provide a detailed exposition of the material to be used. In this material the author not only reviews special topics such as Young measures, the strong-narrow topology and relaxed spaces but also introduces a convexity structure on Young measures by a limit procedure.