On one generalization of a DiPerna and Majda theorem

The weak limits of sequences {f(u(nu))}(nu)(element of) N where u(nu)ʹs are vector-valued (mu)-measurable functions defined on a compact set (omega)and f is (possibly) discontinuous are investigated. As shown by the author (J. Conv. Anal. (to appear)), they are described in terms of integral formulae involving parametrized measures independent of f, similarly as in the classical theorem by Young and its generalization due to DiPerna and Majda. In the present paper we describe the supports of the involved parametrized measures.