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

Generalized version of the Lions-type lemma