Characterizing compact sets in $L^p$-spaces and its application
General Topology
2022-09-27 v3 Functional Analysis
Abstract
In this paper, we give a characterization of compact sets in -spaces on metric measure spaces, which is a generalization of the Kolmogorov-Riesz theorem. Using the criterion, we investigate the topological type of the space consisting of lipschitz maps with bounded supports.
Cite
@article{arxiv.2205.06864,
title = {Characterizing compact sets in $L^p$-spaces and its application},
author = {Katsuhisa Koshino},
journal= {arXiv preprint arXiv:2205.06864},
year = {2022}
}
Comments
The proof of the if part of Theorem 1.3 has been corrected (Propositions 2.4 and 2.6)