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 a sequence of independent copies of a mean zero random variable f 2 Lp spans in Lp a subspace isomorphic to some Orlicz sequence space lM. We present precise connections between M and f and establish conditions under which the dis- tribution of a random variable f 2 Lp whose independent copies span lM in Lp is essentially unique.
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