Solution
= Solution
For each $n\geq1$, choose a countable interval cover of $E_n$ of total length below $\epsilon/2^n$. The union of these covers is countable and covers $\bigcup_n E_n$, with total length less than $\sum_n\epsilon/2^n=\epsilon$. As $\epsilon$ is arbitrary, \b[a countable union of <null sets> is null].