Probably an easy measure theory exercise, but I am drawing a blank. I have done exercises like this before, and I feel like I have wanted to consider a set like $A=|f|^{-1}[1,\infty)$ and split the summation/ integral over $A$ and $A^c$. Doesn't quite seem to be working for me in this case. If anyone has some hints for me that would be excellent.
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