Talk:Radon-Nikodym Theorem

Hadn't realised we already had trace $\sigma$-algebras set up here, (rather, I didn't know the proper name for a $\sigma$-algebra generated by intersections) and the part using the intersection measure might be a bit more aesthetically pleasing doing that instead. (avoiding having to play with the sum at the end) Will try to come back to it later, if anyone's passing by and wants to add it (as part of a Proof 2 with some refactoring I guess) feel free. Caliburn (talk) 15:38, 17 December 2021 (UTC)

Essential Uniqueness
I crated Characterization of Almost Everywhere Zero--Usagiop (talk) 20:27, 10 June 2022 (UTC)
 * This replicates Measurable Function Zero A.E. iff Absolute Value has Zero Integral it looks like. The proof of essential uniqueness is elaborate because the integrals may be infinite, so considering $\int \paren {g_1 - g_2} \rd \mu$ may not make sense. If you work with finite measures, it's as quick as you say. Caliburn (talk) 20:51, 10 June 2022 (UTC)
 * Why is my page replicates Measurable Function Zero A.E. iff Absolute Value has Zero Integral? I do not see any similarity.
 * $\int \paren {g_1 - g_2} \rd \mu$ may not make sense. No, unless $g_1 - g_2$ is integrable. But why are you taking about this? Did I say something to this type of integral?--Usagiop (talk) 20:57, 10 June 2022 (UTC)
 * Oh wait you are right, but I think it replicates some other theorem on here. (at least I remember doing something very similar) It may not have been proved. I will look at this in the morning. Caliburn (talk) 21:13, 10 June 2022 (UTC)
 * OK, it is possible. Anyway this type of claim should be stated somewhere else, not a part of Radon-Nikodym.--Usagiop (talk) 21:31, 10 June 2022 (UTC)