From Arzelà–Ascoli to Riesz–Kolmogorov. (October 2016) - Górka, Przemysław; Rafeiro, Humberto
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.