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Statistics
A Journal of Theoretical and Applied Statistics
Volume 21, 1990 - Issue 4
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Original Articles

An example concerning the convergence of conditional expectations

Pages 609-611 | Received 01 Oct 1988, Published online: 27 Jun 2007
 

Abstract

An example is given of a uniformly integrable stochastic sequence on a prob¬ability space (?Q, , P) which converges almost surely such that under successive con¬ditioning with respect to some sub-a-fields of % it is possible to switch from almost sure

convergence to non-convergence and vice versa. The example shows that in the dominated

convergence theorem for conditional expectations the assumption that the sequence is bounded in absolute value by an integrable random variable cannot be weakened or re¬placed bxr uniform inteorabilit

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