Geodesic
Konvergenz bedingter Erwartungsoperatoren
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 4, pp. 595-607

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Two concepts of convergence for nets of $\sigma$-rings are defined for every Orlicz space $\mathfrak{L}_M^*$, which imply essential, respectively, stochastic convergence of the corresponding conditional expectations of any random variable in $\mathfrak{L}_M^*$. 
@article{TVP_1964_9_4_a1,
     author = {K. Krickeberg},
     title = {Konvergenz bedingter {Erwartungsoperatoren}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {595--607},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {1964},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_4_a1/}
}
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K. Krickeberg. Konvergenz bedingter Erwartungsoperatoren. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 4, pp. 595-607. http://geodesic.mathdoc.fr/item/TVP_1964_9_4_a1/