ON SUBSPACES OF AN ORLICZ SPACE SPANNED BY INDEPENDENT IDENTICALLY DISTRIBUTED FUNCTIONS

Abstract

Subspaces of an Orlicz space LM generated by probabilistically independent copies of a function \(f \in {{L}_{M}}\), \(\int_0^1 {f(t){\kern 1pt} dt} = 0\), 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 LM. 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.