A Generalized Version of the Lions-Type Lemma

Abstract

In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma generalizes some results for a class of Orlicz–Sobolev spaces. What matters here is the behavior of the integral, not the space.