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Strict topologies on measure spaces
Author(s) -
Samea H.,
Fasahat E.
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600227
Subject(s) - mathematics , hausdorff space , subspace topology , lebesgue measure , compact open topology , topological space , locally compact space , topology (electrical circuits) , measure (data warehouse) , space (punctuation) , urysohn and completely hausdorff spaces , general topology , network topology , hausdorff measure , convergence (economics) , outer measure , pure mathematics , discrete mathematics , lebesgue integration , hausdorff dimension , combinatorics , interpolation space , mathematical analysis , fractal , functional analysis , minkowski–bouligand dimension , computer science , database , chemistry , biochemistry , economics , fractal dimension , economic growth , operating system , gene
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.