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Uniform integrability and Young measures. (English) Zbl 0930.28004

Summary: We introduce a new property equivalent to uniform integrability. This property, stated in terms of Young measures, seems rather topological. But it appears to be as powerful as other more quantitative properties. Using the same techniques we give a new proof of a theorem of V. Jalby [“Contribution aux problèmes de convergence des fonctions vectorielles et des intégrales fonctionnelles”, Thèse de Doctorat, Montpellier (1993)]. \(\copyright\) Academic Press.

MSC:

28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
49J45 Methods involving semicontinuity and convergence; relaxation
28A33 Spaces of measures, convergence of measures
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