Consider Lebesgue spaces $L^p(\Omega)$, $\Omega$ is a bounded domain.
Let $f \in L^p(\Omega)$ for all $p$.
Is it true that $f \in L^\infty(\Omega)$?
2026-04-01 08:02:23.1775030543
$L^\infty(\Omega)$ space
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Hint: $\Omega=(0,1)$, $f(x)=\log x$.