We know if $\mu(X)<\infty$, and if $1\le p<q<\infty$, then $L^q(X)\subset L^p(X)$ (can be proved by using Holder's inequality).
Is this still true if $\mu(X)=\infty$? Counterexample? Thanks.
2026-04-18 14:27:15.1776522435
Counterexample to: if $1\le p<q<\infty$, then $L^q(X)\subset L^p(X)$ with $\mu(X)=\infty$
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