Hey guys thank you for helping me, It's vanishing property and finiteness property. and I wanna prove:
$f\ge0$ and $f$ is measurable. Then,
1. $\int fd\lambda=0 \Longleftrightarrow \{x|f(x)>0\}$ is a null set.
2. $\int fd\lambda<\infty \Longrightarrow \{x|f(x)=\infty\}$ is a null set.
I don't know how can I approach. please help me. thx
Integration on measure theory
1
$\begingroup$
real-analysis
measure-theory
-
3Is this homework? – 2012-05-06