Autori: Florescu L.C.
Editorial: Central European Journal of Mathematics , 5(4), p.619-638, 2007.
We introduce two notions of tightness for a set of measurable functions – the finite-tightness and the Jordan finite-tightness with the aim to extend certain compactness results (as biting lemma or Saadoune- Valadier’s theorem of stable compactness) to the unbounded case. These compactness conditions highlight their utility when we look for some alternatives to Rellich-Kondrachov theorem or relaxed lower semicontinuity of multiple integrals.
Finite-tightness locates the great growths of a set of measurable
mappings on a finite family of sets of small measure. In the Euclidean case, the Jordan finite-tight sets form a subclass of finite-tight sets for which the finite family of sets of small
measure is composed by $d$-dimensional intervals. The main result affirms that each tight set H for which the set
of the gradients
abla H is a Jordan finite-tight set is relatively compact in measure. This result offers very good
conditions to use fiber product lemma for obtain a relaxed lower semicontinuity condition.
Cuvinte cheie: finite-tight set, Jordan finite-tight set, Young measure,w^2 - convergence