On Young measures controlling discontinuous functions
Agnieszka Kaïamajska · Journal of convex analysis · 2006
The classical theorem of Young in one of its versions states that if Ω ⊆ R is an open bounded domain, f : R → R is a continuous function vanishing at infinity and u : Ω → R is a sequence of measurable functions which satisfies tightness condition (see formulae (6) below) then there exists a subsequence {u} of {u} such that the sequence {f(u)} converges ∗-weakly in L∞(Ω) to the function f determined by an integral formula