Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 2, Pages 137-146
Fatou's Lemma and Lebesgue's convergence theorem for measures
1CINVESTA V-IPN, Departamento de Matemáticas, Apdo. Postal 14-740, México D.F. 07000, Mexico
2LAAS-CNRS, 7, Avenue Du Colonel Roche, Toulouse Cédex 31077, France
Received 1 December 1998; Revised 1 November 1999
Copyright © 2000 Onésimo Hernández-Lerma and Jean B. Lasserre. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Analogues of Fatou's Lemma and Lebesgue's convergence theorems are
established for when is a sequence of measures. A generalized Dominated Convergence Theorem is also proved for the asymptotic behavior of 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.