Timeline for Convergence of integral averages in $L^1$

9 events

when toggle format	what		by	license	comment
Jul 18, 2022 at 11:43	history	edited	Daniele Tampieri	CC BY-SA 4.0	Embedded link
Jul 18, 2022 at 1:05	history	edited	Yuval Peres	CC BY-SA 4.0	edited body
Jul 18, 2022 at 0:00	comment	added	Nate River		I guess this works because the sup in the maximal function is realised closer and closer to $0$ as $x \to 0$. Furthermore for the failure to be in $L^1$ it needs only not be locally integrable near a point (in this case $0$).
Jul 17, 2022 at 23:57	comment	added	Nate River		Very nice, I would not have come up with a function like that myself!
Jul 17, 2022 at 23:57	vote	accept	Nate River
Jul 17, 2022 at 23:32	history	edited	Yuval Peres	CC BY-SA 4.0	added 443 characters in body
Jul 17, 2022 at 23:16	history	edited	Yuval Peres	CC BY-SA 4.0	added 443 characters in body
Jul 17, 2022 at 16:31	comment	added	Nate River		Interesting, I would’ve thought $g_n \to 0$ uniformly would cause you to be unable to capture the maximal function, since most of the points don’t get to “do what they want”. Looking forward to the counterexample!
Jul 17, 2022 at 15:56	history	answered	Yuval Peres	CC BY-SA 4.0