Open Access
January, 1989 A Convergence Property for Conditional Expectation
Aurel Cornea, Peter A. Loeb
Ann. Probab. 17(1): 353-356 (January, 1989). DOI: 10.1214/aop/1176991513


Convergence properties are obtained for repeated applications of the operator $f \rightarrow |f - E(f)|$, where $E$ denotes conditional expectation. If, for example, $E$ is the integral with respect to a probability measure $P, f \in L^\infty(P)$ and $T(f) = |f - E(f)|$, then $T^n(f)$ converges to 0 in $L^\infty(P)$ and $\Sigma T^n(f)$ converges in $L^1(P)$.


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Aurel Cornea. Peter A. Loeb. "A Convergence Property for Conditional Expectation." Ann. Probab. 17 (1) 353 - 356, January, 1989.


Published: January, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0674.60033
MathSciNet: MR972790
Digital Object Identifier: 10.1214/aop/1176991513

Primary: 28A20
Secondary: 60F25

Keywords: $L^1$ convergence , conditional expectation

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 1 • January, 1989
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