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 Nov25 awarded Popular Question Nov6 awarded Popular Question Sep30 awarded Explainer Jul2 awarded Curious Feb10 awarded Notable Question Jan24 awarded Yearling Oct28 awarded Popular Question Mar13 awarded Popular Question Jan24 awarded Yearling Jun8 awarded Caucus May11 accepted Question on singular measures and absolute continuity May11 revised A Question on Convergence In $L^p$ added 1 characters in body May11 revised A Question on Convergence In $L^p$ added 1 characters in body May11 revised A Question on Convergence In $L^p$ added 1 characters in body May9 comment An application of Riesz Representation Theorem @leo: then $f$ would have to 1. right? May9 comment An application of Riesz Representation Theorem @leo: I don't get your point. Do you mean $\int|g-h|=0$ implies $g=h$? May8 comment How to show a sequence is not uniformly integrable @DavidMitra: How does one find such an $n$? May8 comment If $f$ is measurable and $fg$ is in $L^1$ for all $g \in L^q$, must $f \in L^p$? Thanks very very much. May7 comment If $f$ is measurable and $fg$ is in $L^1$ for all $g \in L^q$, must $f \in L^p$? sorry if I wasn't clear before. I was wondering if you could expand on the derivation of the contradiction. for example why $g=\sum\limits_{k=1}^\infty2^{-k}g_k\|g\|_{L^q}$ is less than one and why it implies that $fg\notin L^1$. May7 comment If $f$ is measurable and $fg$ is in $L^1$ for all $g \in L^q$, must $f \in L^p$? @robjohn: do you mind elaborating on your proof a bit. the part where you showed that $\|fg\|_{L^1} \leq C \|g\|_{L^q}$? Thanks