Abstract
Let 1⩽p<2 and let Lp=Lp[0,1] be the classical Lp-space of all (classes of) p-integrable functions on [0,1]. It is known that any subspace in Lp spanned by a sequence of independent copies of a mean zero random variable f∈Lp is isomorphic to some Orlicz sequence space lN. We employ methods from interpolation theory to fully describe the class of Orlicz functions N which can be obtained by this procedure and to identify the precise connection between N and the distribution of f. Our methods strengthen and complement classical results of M.I. Kadec as well as those of J. Bretagnolle and D. Dacunha-Castelle.
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