Could you please help me with this question:
Prove the following (known as Pratt's Lemma):
Let be sequences of integrable functions. If
3) and as with and both finite,
and is finite.
I was thinking about mimicking the proof of the Dominated Convergence Theorem (noting that and by Fatou's Lemma, concluding that ) but I'm not quite sure where to go from there... Any hints/help is appreciated