DOI: 10.68381/jca04006 ISSN: 0944-6532
Non-Uniform Integrability and Generalized Young Measures
J.J. Alibert, G. Bouchitté
Given a bounded sequence (uₙ) in L¹ (Ω, µ;
\mathbb{R}^d
R
d
), we describe the weak limits in the sense of measures of f(x, uₙ) µ for a class of continuous integrands with linear growth at infinity. The defect of uniform integrability of the sequence f(x, uₙ) is described by a measure m and a family of probability measures on
S^{d-1}
S
d
−
1
whereas the classical Young measure is associated with the biting limits in the sense of Chacon’s lemma. Some consequences of this new approach are given in Calculus of Variations.