Show that if $\displaystyle (f_n)_n$ is a sequence in $\displaystyle L^1[0, 1]$ is such that $\displaystyle \sum_{n=1}^{\infty} || f_n ||_1 < \infty$ then $\displaystyle \sum_{n=1}^{\infty} | f_n(s) | < \infty$ for almost every $\displaystyle s \in [0, 1]$.

This looks simple to prove. However, I do not see how to prove this right now. Any hints on how to proceed would be appreciated.