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Abstract Theorems on Exchange of Limits and Preservation of (Semi)continuity of Functions and Measures in the Filter Convergence Setting

By Antonio Boccuto and Xenofon Dimitriou

Abstract

We give necessary and sufficient conditions for exchange of limits of double-indexed families, taking values in sets endowed with an abstract structure of convergence, and for preservation of continuity or semicontinuity of the limit family, with respect to filter convergence. As a consequence, we give some filter limit theorems and some characterization of continuity and semicontinuity of the limit of a pointwise convergent family of set functions. Furthermore, we pose some open problems

Topics: Mathematics, QA1-939
Publisher: Hindawi Publishing Corporation
Year: 2016
DOI identifier: 10.1155/2016
OAI identifier: oai:doaj.org/article:345138ac1ba64a939b0f22658bc52054
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  • http://dx.doi.org/10.1155/2016... (external link)
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