I am having difficulty proving the following,
Let
Prove that
Background: is the set of complex measurable functions f such that
I will also be using and and a lemma that if f is a positive measurable function then
My Proof thus far: (I have separated the proof into 2 cases)
Case 1:
and this is where I am stuck both so I can apply the lemma stated earlier but I can not split the integral unless both functions are positive but is negative.
Any suggestions on how i can get around this obstacle would be greatly appreciated !