On one generalization of a DiPerna and Majda theorem

摘要

The weak limits of sequences {f(uv)}(nu is an element of N) where u(nu)'s 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. Copyright (C) 2006 John Wiley & Sons, Ltd.