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

Katsuhisa Koshino

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arXiv · 2205.06864

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

Katsuhisa Koshino

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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.

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Katsuhisa Koshino. 2022-05-13. Characterizing compact sets in $L^p$-spaces and its application. https://arxiv.org/abs/2205.06864

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