zbMATH — the first resource for mathematics

Young measures. (English) Zbl 0738.28004
Methods of nonconvex analysis, Lect. 1st Sess. CIME, Varenna/Italy 1989, Lect. Notes Math. 1446, 152-188 (1990).
[For the entire collection see Zbl 0705.00022.]
This paper is a survey on Young measures. The main idea is that Young measures generalize functions and are particularly useful to study the limit behaviour of a sequence of oscillating functions. Under very mild assumptions any sequence of functions has a subsequence which converges to some Young measure.
The titles of the six sections are: First level theory: examples; Second level theory: the measurable locally compact case; General theory: the case of a metrizable Souslin space. Tightness; Application to sequences of measurable functions; Applications to uniformly integrable sequences in \(L^ 1\); Some properties of bounded sequences in \(L^ 1\). Connection with the biting lemma. An appendix contains some basic results of measure theory.

28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
28A33 Spaces of measures, convergence of measures
49Q20 Variational problems in a geometric measure-theoretic setting
46E27 Spaces of measures
28-02 Research exposition (monographs, survey articles) pertaining to measure and integration
49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control