Convergence in mean of weighted sums of {an,k}-compactly uniformly integrable random elements in Banach spaces
1997 ◽
Vol 20
(3)
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pp. 443-450
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Keyword(s):
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.
Keyword(s):
1979 ◽
Vol 2
(2)
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pp. 309-323
1999 ◽
Vol 22
(3)
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pp. 559-568
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2001 ◽
Vol 51
(2)
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pp. 155-164
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Keyword(s):
1983 ◽
Vol 6
(1)
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pp. 69-79
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2006 ◽
Vol 2006
◽
pp. 1-6
2016 ◽
Vol 160
(3)
◽
pp. 413-421
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2002 ◽
Vol 47
(3)
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pp. 533-547
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