Abstract Theorems on Exchange of Limits and Preservation of (Semi)continuity of Functions and Measures in the Filter Convergence Setting. (13th July 2016)

• Record Type: Journal Article
• Authors: Boccuto, Antonio; Dimitriou, Xenofon
• Other Names: Rasa Ioan Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-07-13
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/4237423
• Languages: English
• ISSNs: 2314-8896

Abstract

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.