Fatou's Lemma and Lebesgue's convergence theorem for measures. (2000) - Hernández-Lerma, Onésimo; Lasserre, Jean B.
Abstract : Analogues of Fatou's Lemma and Lebesgue's convergence theorems are established for ∫ f d μ n when { μ n } is a sequence of measures. A generalized Dominated Convergence Theorem is also proved for the asymptotic behavior of ∫ f n d μ n and the latter is shown to be a special case of a more general result established in vector lattices and related to the Dunford-Pettis property in Banach spaces.