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

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

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Article ID: iaor20022073
Country: United States
Volume: 13
Issue: 2
Start Page Number: 137
End Page Number: 146
Publication Date: Apr 2000
Journal: Journal of Applied Mathematics and Stochastic Analysis
Authors: ,
Keywords: probability
Abstract:

Analogues of Fatou's Lemma and Lebesgue's convergence theorems are established for ∫ fdμn when {μn} is a sequence of measures. A ‘generalized’ Dominated Convergence Theorem is also proved for the asymptotic behavior of ∫ fndμn 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.

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