Uniformity in convergence of measures

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1977 English Publisher:Springer Science and Business Media LLCJournal:Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, volume 39, pages 1-30 (issn: 0044-3719, eissn: 1432-2064,

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Authors: Topsøe, Flemming;

doi: 10.1007/bf01844870

Uniformity in convergence of measures

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Abstract

Assume that a net (σα) of measures converges in some sense to a measureΜ. Then we investigate whether for a given class ℰ of functions, we can conclude that $$\mathop {\lim }\limits_\alpha \mathop {\sup }\limits_{f \in E} |\int {fd\mu _\alpha } - \int {fd\mu } | = 0.$$ .

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BIO5 Institute
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Keywords

Limit theorems in probability theory, Convergence of probability measures, Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence

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