Characterizing compact sets in $L^p$-spaces and its application

Abstract

In this paper, we give a characterization of compact sets in $L^p$-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.

arXiv commentThe proof of the if part of Theorem 1.3 has been corrected (Propositions 2.4 and 2.6)