Fatou's Lemma and Lebesgue's convergence theorem for measures. (2000)

• Record Type: Journal Article
• Authors: Hernández-Lerma, Onésimo; Lasserre, Jean B.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 13:Number 2(2000)
• Page Start: 137
• Page End: 146
• Publication Date: 2000
• Subjects: measures -- Fatou and Lebesgue's theorems -- AM-spaces -- AL-spaces; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953300000150
• Languages: English
• ISSNs: 1048-9533

Abstract

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.