$A \subseteq \mathbb R$ is *strong measure zero* if given any sequence $( \epsilon\_n )\_{n \in \mathbb N}$ of positive reals there is a sequence $( I\_n )\_{n \in \mathbb N}$ of open intervals such that $I\_n$ has length at most $\epsilon\_n$ for each $n$, and $A \subseteq \bigcup\_{n \in \mathbb N} I\_n$.

I have read that the Cantor set is an example of a null set which is not strong measure zero.

Can anyone explain why or direct me to a reference which contains a proof?