Affiliation:
1. Department of Mathematical Analysis, University of Sevilla, Sevilla, Spain
Abstract
The convergence in mean of a weighted sum∑kank(Xk−EXk)of random elements in a separable Banach space is studied under a new hypothesis which relates the random elements with their respective weights in the sum: the{ank}-compactly uniform integrability of{Xn}. This condition, which is implied by the tightness of{Xn}and the{ank}-uniform integrability of{‖Xn‖}, is weaker than the compactly miform integrability of{Xn}and leads to a result of convergence in mean which is strictly stronger than a recent result of Wang, Rao and Deli.
Subject
Mathematics (miscellaneous)
Cited by
9 articles.
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