Orlicz sequence spaces spanned by identically distributed independent random variables in LpLp-spaces

Let 1⩽p<21⩽p<2 and let Lp=Lp[0,1]Lp=Lp[0,1] be the classical LpLp-space of all (classes of) p  -integrable functions on [0,1][0,1]. It is known that any subspace in LpLp spanned by a sequence of independent copies of a mean zero random variable f∈Lpf∈Lp is isomorphic to some Orlicz sequence space lNlN. 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.