Convergence of Generalized Entropy Minimizers in Sequences of Convex Problems

Integral functionals based on convex normal integrands are minimized over convex constraint sets. Generalized minimizers exist under a boundedness condition. Sequences of the minimization problems are studied when the constraint sets are nested. The corresponding sequences of generalized minimizers are related to the minimization over limit convex sets. Martingale theorems and moment problems are discussed.