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Convergence in mean of weighted sums of { a n,k }-compactly uniformly integrable random elements in Banach spaces

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  • M. Ordóñez Cabrera

Abstract

The convergence in mean of a weighted sum ∑ k a n k ( X k − E X k ) 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 { a n k } -compactly uniform integrability of { X n } . This condition, which is implied by the tightness of { X n } and the { a n k } -uniform integrability of { ‖ X n ‖ } , is weaker than the compactly miform integrability of { X n } and leads to a result of convergence in mean which is strictly stronger than a recent result of Wang, Rao and Deli.

Suggested Citation

  • M. Ordóñez Cabrera, 1997. "Convergence in mean of weighted sums of { a n,k }-compactly uniformly integrable random elements in Banach spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:436456
    DOI: 10.1155/S0161171297000604
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