justin_huang
May18-11, 04:31 PM
let f: X\rightarrow [0,1] be a positive, measurable function on a sigma-finite measure space (X,A,u). If p>0, show that
\int f^{p} d\mu=p \int^{\infty}_{0} t^{p-1} dt (x\in X:f(x)>t)
\int f^{p} d\mu=p \int^{\infty}_{0} t^{p-1} dt (x\in X:f(x)>t)