Re: Question about convergence in Lp

In article <1140395567.431377@xxxxxxxxxxxxx>,
Hans Jensen <jjjg3401@xxxxxxxxx> wrote:

I have a question about convergence. Let f,f_k be in L^p 1<= p <
\infty. Assuming that f_k -> f point wise a.e. and that ||f_k||_p ->
||f||_p, is it true that ||f_k - f|| -> 0 ? If yes, how can one prove this?

Yes, try Fatou's Lemma applied to C(|f_n|^p + |f|^p) - |f_n -
f|^p, where C is chosen so that this expression is nonnegative.
.