Give an example in $\displaystyle [0, 1]$ of a sequence of measurable functions $\displaystyle (f_n)_n$ such that $\displaystyle \lim_{n \rightarrow \infty } || f_n ||_1=0$ but $\displaystyle (f_n)_n$ does not converge to zero a.e.

For this one, I can't think of a sequence that fits this criteria. What would this sequence look like? I can't think of one right now.