Past exam of the options I course of the University of Oxford / 2005 / D / 1 / i

A set $E\subseteq [0,1]$ is null when for every $\epsilon >0$ it can be covered by countably many open intervals whose lengths sum to less than $\epsilon$. Equivalently its Lebesgue outer measure is zero. This definition does not presuppose measurability of $E$.