Weak conditions are presented for approximating dynamic programming models. For a sequence of these models, continuous convergence of the sequence of associated optimal value functions is obtained under the condition that state and action space converge in the sense of Kuratowski, and that the mappings of admissible actions as well as the transition law, the discount factors and the reward functions converge continuously. Further a relation for the associated sets of optimal actions is given. The analysis is based on results about convergence preserving properties of supremum value functions and integrals. The approximation results are extended to so-called upper-semi-continuous convergent sequences and are related to discretization procedures by using projections.
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