I am looking for literature that states/discusses/proves the following result on nonatomic measure spaces: "Let $0<p<1$. The only convex subset of $L^{p}(μ)$ with non-empty interior is the set $L^{p}(μ)$ itself." Thanks.
2026-04-07 21:38:22.1775597902
Literature on convex subsets of Lp spaces with 0<p<1
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Para 1.47 in Rudin, W. (1991) Functional Analysis. 2nd edition. New York: McGraw-Hill. Thanks to Soma.