From Arzelà–Ascoli to Riesz–Kolmogorov. (October 2016)

• Record Type: Journal Article
• Authors: Górka, Przemysław; Rafeiro, Humberto
• Is Part Of: Nonlinear analysis. Volume 144(2016)
• Page Start: 23
• Page End: 31
• Publication Date: 2016-10
• Subjects: 28C99 -- 46B50 -- 46E30; Banach function spaces -- Metric measure spaces -- Riesz–Kolmogorov theorem -- Grand variable exponent Lebesgue spaces; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.06.004
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study totally bounded sets in Banach function spaces (BFS), from which we characterize compact sets (via Hausdorff criterion) in some non-standard function spaces which fall under the umbrella of BFS. We obtain a Riesz–Kolmogorov compactness theorem for the grand variable exponent Lebesgue spaces.