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

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