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Nov 9 at 14:38 comment added Marc @Victor Since we only need the convergence on compact subsets, it is enough to show it on a fixed compact, and use a diagonal argument.
Nov 9 at 12:56 comment added Victor Why is it possible to apply Calderón - Zygmund so directly in $L^p$? I mean, following corollary 9.18 of trudinger it's possible to apply the estimate only when $f_n- \mu \in L^p$ for $p>1$, but in the situation of the theorem we have $f_n-\mu \in L^{p}_{loc}$
Apr 3, 2023 at 19:26 vote accept User1723
Apr 3, 2023 at 2:53 history edited Marc CC BY-SA 4.0
Corrected reference
Apr 3, 2023 at 1:30 history answered Marc CC BY-SA 4.0