Analogues of Fatou's Lemma and Lebesgue's convergence theorems are established for∫fdμnwhen{μn}is a sequence of measures. A “generalized” Dominated Convergence Theorem is also proved for the asymptotic behavior of∫fndμnand 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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