Timeline for Radon-Nikodym derivative of pushforward of Lebesgue measure by differentiable function with respect to Lebesgue measure
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21 events
| when toggle format | what | by | license | comment | |
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| Nov 21, 2022 at 0:59 | answer | added | jII | timeline score: 2 | |
| Oct 18, 2022 at 17:15 | comment | added | jII | Note that when $f$ is a diffeomorphism it must be that $n = m$. | |
| S Apr 4, 2022 at 16:19 | history | bounty ended | Euler_Salter | ||
| S Apr 4, 2022 at 16:19 | history | notice removed | Euler_Salter | ||
| Apr 1, 2022 at 3:03 | comment | added | Mason | Look at the area and coarea formulas in the measure theory book by Evans and Gariepy. | |
| Mar 31, 2022 at 18:50 | history | edited | Euler_Salter | CC BY-SA 4.0 |
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| Mar 31, 2022 at 18:00 | history | tweeted | twitter.com/StackMath/status/1509591401947873281 | ||
| Mar 30, 2022 at 5:44 | answer | added | Max | timeline score: 4 | |
| S Mar 28, 2022 at 8:37 | history | bounty started | Euler_Salter | ||
| S Mar 28, 2022 at 8:37 | history | notice added | Euler_Salter | Canonical answer required | |
| Mar 24, 2022 at 14:46 | comment | added | Euler_Salter | @Ilya I expected it too but I checked Federer's, Billingsley and more books but found nothing.. perhaps it has another name | |
| Mar 24, 2022 at 14:46 | history | edited | Euler_Salter | CC BY-SA 4.0 |
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| Mar 24, 2022 at 14:45 | comment | added | Euler_Salter | @bs_math good point, I forgot about that. I will add it to the assumptions | |
| Mar 24, 2022 at 14:44 | comment | added | bs_math | Note that the Radon-Nikodym derivative $\frac{df_* \lambda^n}{d\lambda^m}$ only exists if $f_* \lambda^n$ is absolutely continuous with respect to $\lambda^m$. So for example if $f$ is constant the derivative will not exist. | |
| Mar 24, 2022 at 14:42 | comment | added | SBF | I'd expect some GMT books, like Federer's. Not my field, I was a bit more into general MT. | |
| Mar 24, 2022 at 14:41 | comment | added | Euler_Salter | @Ilya do you have any idea if the statement I make for $f$ differentiable is true? And where I could find a reference to it? | |
| Mar 24, 2022 at 14:32 | comment | added | SBF | Ah, I've missed the point that you don't drop smoothness, you have difference in dimensions. That nevermind my previous comment. | |
| Mar 24, 2022 at 14:28 | comment | added | Euler_Salter | @Ilya I'm not sure what you mean sorry.. | |
| Mar 24, 2022 at 14:26 | history | edited | Euler_Salter | CC BY-SA 4.0 |
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| Mar 24, 2022 at 14:25 | comment | added | SBF | If you lose smoothness, usually integration helps | |
| Mar 24, 2022 at 14:19 | history | asked | Euler_Salter | CC BY-SA 4.0 |