If we have a bounded sequence $\{f_n\} \in L^p[a,b]$ that converges weakly to $f$ does this mean that the converges is also pointwise??
thank you.
2026-03-29 23:40:46.1774827646
weak convergence implies point-wise convergence?
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No. Just take $f_n\in L^2[0,1]$, $f_n = \sin(n\pi x)$. Then $f_n\rightharpoonup0$ in $L^2[0,1]$.