Question about convergence in Lp

From: Hans Jensen <jjjg3401@xxxxxxxxx>
Date: Sun, 19 Feb 2006 18:28:40 -0600

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?

/Hans
.

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