# proof of Fatou-Lebesgue theorem

## Primary tabs

Major Section:
Reference
Type of Math Object:
Proof

## Mathematics Subject Classification

### non-negative

How are we able to apply Fatou's lemma in this proof? The conditions of Fatou's lemma clearly state we need a non-negative sequence of measurable functions yet here we are not given the non-negativeness of fn. How is this reconciled?

### Re: non-negative

This is reconciled by considering the sequence \phi+f_n, which must necessarily be nonnegative. I admit that I overlooked this and will edit the proof accordingly when I have more time.