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Fatou's Lemma and Lebesgue's convergence theorem for measures

Onésimo Hernández-Lerma and Jean B. Lasserre

International Journal of Stochastic Analysis, 2000, vol. 13, 1-10


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.

Date: 2000
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DOI: 10.1155/S1048953300000150

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