Series of independent,mean zero random variables in rearrangement-invariant spaces having the Kruglov property

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, ∞). The 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 the isomorphism between rearrangement-invariant spaces on 0, 1] and 0, ∞). Bibliography: 20 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 345, 2007, pp. 25–50.