We study Banach function spaces (BFS) on locally compact topological groups. We focus on totally bounded sets in BFS. We obtain the Riesz–Kolmogorov compactness theorem as well as the Sudakov theorem.
"Banach function spaces on locally compact groups." Ann. Funct. Anal. 10 (4) 460 - 471, November 2019. https://doi.org/10.1215/20088752-2019-0002