On Subspaces of an Orlicz Space Spanned by Independent Identically Distributed Functions

Abstract

Abstract: Subspaces of an Orlicz space L<inf>M</inf> 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 L<inf>M</inf>. 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. © 2023 Elsevier B.V., All rights reserved.