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A Note on the Vague Topology for Measures
Published online by Cambridge University Press: 24 October 2008
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We refer for general background to N. Bourbaki, Intégration, chapters iv and v. We consider a locally compact Hausdorff space R and denote the set of continuous functions with compact support by The Riesz-Markov theorem shows that there is a 1−1 correspondence between the set of regular Borel measures on R and the set of positive elements of the topological dual of . Let {μn}, μ be regular Borel probability measures on R. The sequence of measures {μn} is said to converge vaguely to μ if, for all . Thus the vague topology is that of simple convergence in . We shall call a μ-measurable set μ-quarrable if its boundary is a μ-null set.
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- Research Notes
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- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 2 , April 1962 , pp. 421 - 422
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- Copyright © Cambridge Philosophical Society 1962
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