Geodesic
Series of independent mean zero random variables in rearrangement invariant spaces with the Kruglov property
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 35, Tome 345 (2007), pp. 25-50 
S. V. Astashkin; F. A. Sukochev. Series of independent mean zero random variables in rearrangement invariant spaces with the Kruglov property. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 35, Tome 345 (2007), pp. 25-50. http://geodesic.mathdoc.fr/item/ZNSL_2007_345_a1/
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     author = {S. V. Astashkin and F. A. Sukochev},
     title = {Series of independent mean zero random variables in rearrangement invariant spaces with the {Kruglov} property},
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     year = {2007},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_345_a1/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

This paper compares sequences of independent mean zero random variables in a rearrangement invariant space $X$ on $[0,1]$ with sequences of disjoint copies of individual terms in the corresponding rearrangement invariant space $Z_X^2$ on $[0,\infty)$. Principal results of the paper show that these sequences are equivalent in $X$ and $Z_X^2$ respectively if and only if $X$ possesses the (so-called) Kruglov property. We also apply our technique to complement well-known results concerning isomorphism between rearrangement invariant spaces on $[0,1]$ and $[0,\infty)$.

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