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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
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 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
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 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 Westbury Jan 25 2012 at 8:12

1 Answer

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The question is not very clear. Please determine what A, B and C are?

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Dear Maliheh, A,B and C are $L^p$ functions. – Sarah Grady Jan 25 2012 at 6:52
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 Dear Maliheh, please do not leave comments as answers, the software is not set up for this. If you do not have sufficient reputation to leave comments, please wait until you do – Yemon Choi Jan 25 2012 at 7:05

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