Abstract theorems on exchange of limits and preservation of (semi)continuity of functions and measures in the filter convergence setting

DOI10.1155/2016/4237423zbMath1365.40006OpenAlexW2344743206WikidataQ59127009 ScholiaQ59127009MaRDI QIDQ530258

Xenofon Dimitriou, Antonio Boccuto

Publication date: 29 July 2016

Published in: Journal of Function Spaces (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2016/4237423

zbMATH Keywords

filter convergencecone metric spaceconvergence of set functions

Mathematics Subject Classification ID

Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Convergence and divergence of infinite limiting processes (40A99) Set functions, measures and integrals with values in ordered spaces (28B15)

Cites Work

• Korovkin-type theorems for abstract modular convergence
• Semicontinuous limits of nets of continuous functions
• Abstract Korovkin-type theorems in modular spaces and applications
• Geodesics in asymmetric metric spaces
• Filter convergence and decompositions for vector lattice-valued measures
• Decomposition of topologies which characterize the upper and lower semicontinuous limits of functions
• A unified theory of cone metric spaces and its applications to the fixed point theory
• Convergence of partial maps
• Ascoli-type theorems in the cone metric space setting
• A convergence-theoretic viewpoint on the Arzelá-Ascoli theorem
• Strong uniform continuity
• Convergence Theorems for Lattice Group-Valued Measures
• Generalized Measure Theory
• A Direct Proof of the Matthes-Wright Integral Extension Theorem
• (Strong) weak exhaustiveness and (strong uniform) continuity
• Uniform \(s\)-boundedness and convergence results for measures with values in complete l-groups
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