For an upper semi-continuous set-valued mapping from one topological space to another and for a lower semi-continuous function defined on the product of these spaces, Berge’s theorem states lower… (More)

S f(s)μ(ds) = 1, ∫ S f(s)μn(ds) = 0, and (1.3) does not hold. Theorem 1.1 presents Fatou’s lemma for weakly converging measures μn and nonnegative functions fn. This fact is useful for the analysis… (More)

This paper presents sufficient conditions for the existence of stationary optimal policies for average cost Markov decision processes with Borel state and action sets and weakly continuous transition… (More)

and Applied Analysis 3 an evolution triple V ⊂ H ⊂ V ∗ see, e.g., 8 with dense and compact embeddings. We denote by 〈·, ·〉V the duality of V and its dual V ∗, by ‖ · ‖V ∗ the norm in V ∗. We have 〈u,… (More)