Print Email Facebook Twitter Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures Title Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures Author Hille, S.C. Szarek, T. Worm, D.T.H. Ziemlanska, M.A. Publication year 2021 Abstract Various equicontinuity properties for families of Markov operators have been – andstill are – used in the study of existence and uniqueness of invariant probability forthese operators, and of asymptotic stability. We prove a general result on equivalenceof equicontinuity concepts. It allows comparing results in the literature and switchingfrom one view on equicontinuity to another, which is technically convenient in proofs.More precisely, the characterisation is based on a ‘Schur-like property’ for measures: if asequence of finite signed Borel measures on a Polish space is such that it is bounded intotal variation norm and such that for each bounded Lipschitz function the sequence ofintegrals of this function with respect to these measures converges, then the sequenceconverges in dual bounded Lipschitz norm to a measure. Subject Markov operatorsEquicontinuityMeasureDual bounded Lipschsitz normWeak topologySchur property To reference this document use: http://resolver.tudelft.nl/uuid:b7168732-f935-4a26-9a9d-030348e8c08b TNO identifier 946571 Publisher Elsevier B.V. ISSN 0167-7152 Source Statistics and Probability Letters, 169 (169) Document type article Files To receive the publication files, please send an e-mail request to TNO Library.