## Real Analysis Convergence questions [closed]

My question is if A converges to B a.e and B converges to C weakly in $L^p$, then can I conclude A converges to C a.e?

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is this an exercise from a course or a book? – Yemon Choi Jan 25 2012 at 4:49
Dear Yemon. It is not an exercise problem. But, I am sure it is a trivial problem for most of you. Sorry :) – Sarah Grady Jan 25 2012 at 5:07
try math.stackexchange.com/… – Will Jagy Jan 25 2012 at 5:29
I wouldn't say it's trivial, but it is a standard question, especially if you have seen Mazur's theorem on the weak and norm closures of convex sets in Banach spaces. By the way, what is A meant to be? a function? a sequence? a net? – Yemon Choi Jan 25 2012 at 5:30
What sort of functions? And how does a function converge to another function? – David Roberts Jan 25 2012 at 6:46
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## closed as too localized by Will Jagy, Anthony Quas, Yemon Choi, Deane Yang, Bruce WestburyJan 25 2012 at 8:12

Dear Maliheh, A,B and C are $L^p$ functions. – Sarah Grady Jan 25 2012 at 6:52