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Media type:
E-Article
Title:
A Convergence Property for Conditional Expectation
Contributor:
Cornea, Aurel;
Loeb, Peter A.
imprint:
Institute of Mathematical Statistics, 1989
Published in:The Annals of Probability
Language:
English
ISSN:
0091-1798
Origination:
Footnote:
Description:
<p>Convergence properties are obtained for repeated applications of the operator f → |f - E(f)|, where E denotes conditional expectation. If, for example, E is the integral with respect to a probability measure P, f ∈ L<sup>∞</sup>(P) and T(f) = |f - E(f)|, then T<sup>n</sup>(f) converges to 0 in L<sup>∞</sup>(P) and Σ T<sup>n</sup>(f) converges in L<sup>1</sup>(P).</p>