On subspaces of an Orlicz space spanned by independent identically distributed functions

Subspaces of an Orlicz space $L_M$ generated by probabilistically independent copies of a function $f\in L_M$, $\int_0^1f(t)\,dt=0$, are studied. In terms of dilations of $f$, we get a characterization of strongly embedded subspaces of this type and obtain conditions that guarantee that the unit ball of such a subspace has equi-absolutely continuous norms in $L_M$. A class of Orlicz spaces such that for all subspaces generated by independent identically distributed functions these properties are equivalent and can be characterized by Matuszewska–Orlicz indices is determined.