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

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 tot he Dunford-Pettis property in Banach spaces. ©2000 by North Atlantic Science Publishing Company.