# measure theory question about sum of sequence of functions

Let $(f_n)_{n\ge1}$ be a sequence of measurable real valued functions. Prove that there exist a sequence of constants $c_n$ $>0$ such that $\sum_{i=1}^{\infty} c_nf_n$ converges for almost every x $\in \mathbb R$

Any hints is appreciated Thanks

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Try choosing $c_n$ so that $m(\{c_n |f_n| \ge 2^{-n}\}) \le 2^{-n}$. –  Nate Eldredge Nov 2 '12 at 3:15
@NateEldredge: a small correction: choose $c_n$ so that $m\{|x|\le n:c_n|f_n(x)|\ge 2^{-n}\}\le 2^{-n}$. –  23rd Nov 2 '12 at 6:40
@richard why don't you post this as the answer? –  Norbert Nov 2 '12 at 6:47
@Norbert: because Nate Eldredge had almost shown the answer as a comment. –  23rd Nov 2 '12 at 6:52
@richard: Thanks! Could you go ahead and post as an answer? –  Nate Eldredge Nov 2 '12 at 12:33