Weak convergence using Young measures
type: Item
instance of: scholarly article
title: Weak convergence using Young measures
zbMATH Open document ID: 0939.28002
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 2000-07-05T00:00:00Z
review text: 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.
reviewed by: Heinz-Albrecht Klei
Mathematics Subject Classification ID: 28A33
Mathematics Subject Classification ID: 46E27
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 1251467
zbMATH Keywords: convergence properties
zbMATH Keywords: Young measures
zbMATH Keywords: transition probabilities
author: C. Castaing
author: Michel Valadier
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1251467