New fundamentals of Young measure convergence
Erik J. Balder · 1999
This paper presents a new, penetrating approach to Young measure convergence in an abstract, measure theoretical setting. It was started in [12, 13, 14] and given its definitive shape in [18, 22]. This approach is based on K-convergence, a device by which narrow convergence on P(R) can be systematically transferred to Young measure convergence. Here P(R) stands for the set of all probability measures on R (in the sequel, a much more general topological space S is used instead of R). Recall that in this context Young measures are measurable functions from an underlying finite measure space (Ω,A, μ) into P(R). Recall also from [12], [13] (see also [24]) that K-convergence takes the following form when applied to Young measures (see Definition 3.1): A sequence (δk) of Young measures K-converges to a Young measure δ0 [notation: δk K −→ δ0] if for every subsequence (δkj ) of (δk) the following pointwise Cesaro-type convergence takes places