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 , , 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.