Some Embedding Theorems for Modular Classes

Abstract

In 1961 there were obtained results [1] concerning connections between the sets $\cap _{i = 1}^\infty$ L^φi <a,b> and L^ψ<a,b>, where L^φi<a,b> and L^ψ<a,b> are Orlicz classes. These results were successively generalized in [2], [3] and [4], based on the notion of σ-absorbed resp. σ-absorbing families of sets. Here, we observe that the latter result may be extended by replacing families of sets by families of functionals.