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May 4, 2021 at 17:20 comment added Mateusz Kwaśnicki Yes, that is the idea of the argument. And sorry for the typo.
May 4, 2021 at 17:19 history edited Mateusz Kwaśnicki CC BY-SA 4.0
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May 4, 2021 at 13:02 comment added alvarezpaiva BTW, I think there is no $u$ in the numerator in the next to last integral.
May 4, 2021 at 12:50 comment added alvarezpaiva Let me see if I'm getting this from the conceptual viewpoint: forgetting some multiplicative constants, Fedor Petrov's change of variables makes the integral into the Riemann-Liouville integral $I^{1/2} g$, then you use the $I^{1/2} I^{1/2} = I^1$ relation to show that the antiderivative of $g$ must be zero. Is that an accurate summary?
May 4, 2021 at 11:53 comment added alvarezpaiva @MateuszKwaśnicki, that's lovely !!
May 4, 2021 at 11:52 vote accept alvarezpaiva
May 4, 2021 at 8:23 comment added Mateusz Kwaśnicki @FedorPetrov: Right, of course. And so my contribution to this answer decreased to 1/3. :-)
May 4, 2021 at 8:03 comment added Fedor Petrov ...and since $g$ is continuous, almost everywhere yields everywhere
May 4, 2021 at 7:26 history answered Mateusz Kwaśnicki CC BY-SA 4.0