Young measures. (English) Zbl 0738.28004

Valadier, Michel

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.

Reviewer: M.Grüter (Saarbrücken)

MSC:

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

Keywords:

generalized solutions; compactness; transition probability; survey; Young measures; metrizable Souslin space; tightness; sequences of measurable functions; uniformly integrable sequences; bounded sequences; biting lemma

Citations:

Zbl 0705.00022