Strict topologies on measure spaces

H. Samea and E. Fasahat

Mathematische Nachrichten, 2017, vol. 290, issue 17-18, 3020-3028

Abstract: Let X be a measurable space, let B be a family of measurable subsets of it, and let X be a subspace of complex measures on X that is also closed under restrictions of measures. In this paper we introduce the B†convergence topology τ(X,B) and the B†strict topology β(X,B) on X. Among other results, we find necessary and sufficient conditions for Hausdorff†ness and coincide†ness of these topologies. Applications to Lebesgue spaces, and also examples in Hausdorff topological spaces and locally compact groups are given.

Date: 2017
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https://doi.org/10.1002/mana.201600227

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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:290:y:2017:i:17-18:p:3020-3028

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