Closedness of convex sets in Orlicz spaces with applications to dual representation of risk measures

摘要

We study various types of closedness of convex sets in an Orlicz space L-Phi and its heart H-Phi and their relations to a natural version of the Krein-Smulian property. Let L-Psi be the conjugate Orlicz space and H-Psi be the heart of L-Psi. Precisely, we show that the following statements are equivalent: