A Convergence Property for Conditional Expectation
Cornea, Aurel ; Loeb, Peter A.
Ann. Probab., Tome 17 (1989) no. 4, p. 353-356 / Harvested from Project Euclid
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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 $L^1(P)$.
Publié le : 1989-01-14
Classification:  Conditional expectation,  $L^1$ convergence,  28A20,  60F25 
@article{1176991513,
     author = {Cornea, Aurel and Loeb, Peter A.},
     title = {A Convergence Property for Conditional Expectation},
     journal = {Ann. Probab.},
     volume = {17},
     number = {4},
     year = {1989},
     pages = { 353-356},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991513}
}

Cornea, Aurel; Loeb, Peter A. A Convergence Property for Conditional Expectation. Ann. Probab., Tome 17 (1989) no. 4, pp.  353-356. http://gdmltest.u-ga.fr/item/1176991513/