TY - JOUR
T1 - From Arzelà–Ascoli to Riesz–Kolmogorov
AU - Górka, Przemysław
AU - Rafeiro, Humberto
N1 - Funding Information:
H. Rafeiro was partially supported by Pontificia Universidad Javeriana under the research project “Study of non-standard Banach spaces”, ID PPT: 6326 . The authors also thank the anonymous referee for careful reading and very useful comments.
Publisher Copyright:
© 2016 Elsevier Ltd
PY - 2016/10/1
Y1 - 2016/10/1
N2 - 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.
AB - 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.
KW - Banach function spaces
KW - Grand variable exponent Lebesgue spaces
KW - Metric measure spaces
KW - Riesz–Kolmogorov theorem
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U2 - 10.1016/j.na.2016.06.004
DO - 10.1016/j.na.2016.06.004
M3 - Article
AN - SCOPUS:84977073956
VL - 144
SP - 23
EP - 31
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
ER -