I am currently reading a proof where the author uses the following equality. $$\int_0^1g(t)^rdt=r\int_0^\infty\vert\{g>u\}\vert u^{r-1}du$$ Here, $g$ is some positive measurable function and $r$ is a positive real number. I would be happy if someone could explain or prove that to me, or tell me how this equality is called, if it has a name.
Asked
Active
Viewed 38 times
0
-
1It's common in probability, I don't know if it has any names though. See here for example. – Jakobian Nov 10 '18 at 13:12
-
1This is related. – Jakobian Nov 10 '18 at 13:36