Remark on norm compactness in $L^p(μ, X)$
Year: 2020
Type: preprint
Abstract: We prove a compactness criterion in $L^p(μ,X)$: a subset of $L^p(μ,X)$ is relatively norm compact iff the set of integrals of its functions over any measurable set is relatively norm compact, it satisfies the Fréchet oscillation restriction condition and it is p-uniformly integrable. The proof is elementary.
Source: arXiv (Cornell University)
Author: Askoura, Youcef
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394652599