Abstract:The purpose of this note is to discuss the relationship among Rosenthal's modulus of uniform integrability, Young measures and DiPerna-Majda measures. In particular, we give an explicit characterization of this modulus and state a criterion of the uniform integrability in terms of these measures. Further, we show applications to Fatou's lemma.
Keywords: bounded sequences, DiPerna-Majda measures, Fatou's lemma, relative sequential weak compactness, uniform integrability, Young measures
AMS Subject Classification: 28A05, 28A20, 28A33, 40A30