Abstract
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 2X on [0, ∞). The principal results of the paper show that these sequences are equivalent in X and Z 2X , respectively, if and only if X possesses the (so-called) Kruglov property. We also apply our technique to complement well-known results concerning the isomorphism between rearrangement-invariant spaces on [0, 1] and [0, ∞). Bibliography: 20 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 345, 2007, pp. 25–50.
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Astashkin, S.V., Sukochev, F.A. Series of independent, mean zero random variables in rearrangement-invariant spaces having the Kruglov property. J Math Sci 148, 795–809 (2008). https://doi.org/10.1007/s10958-008-0026-z
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DOI: https://doi.org/10.1007/s10958-008-0026-z