Weak convergence using Young measures (Q1279998)

Let \((\Omega,{\mathcal A},P)\) be a probability space and \(X\) a Polish space. A Young measure on \(\Omega\times X\) is defined as a positive measure on (\(\Omega\times X\), \({\mathcal A}\otimes{\mathcal B}(X)\)) whose marginal distribution on \(\Omega\) equals \(P\). Young measures can be identified with transition probabilities or scalarly measurable functions from \(\Omega\) to \(M^1_+(X)\), the set of probability measures on \(X\) endowed with the topology \(\sigma(M^1_+(X), C_b(X))\). Convergence properties of sequences of Young measures are obtained by imbedding \(M^1_+(X)\) in a dual Banach space.