# Thread: an extended real-valued function

1. ## an extended real-valued function

Let
f : X ->[- infinity, infinity] be an extended real-valued function defined on a

measure space
( X, F, m) . Prove that {x : f (x ) > -infinity}
is in segma-algebra F ,and {x: - infinity< f(x)< infinity}
is in segma-algebra F

how can I apply the definition of an extended real-valued function to prove this, any help would be appraciated.
Thanks,

2. any idea how to solve it would be appreciated

3. It seems like you're missing something from your problem statement, because unless F=P(X), we can choose some subset A of X such that A is not in F, and define f by

$f(x)=\begin{cases}0&x\in A\\-\infty&x\notin A.\end{cases}$

Maybe f is supposed to be measurable?