Past exam of the options II for mathematics and philosophy course of the University of Oxford / 2013 / D4 / a / i

A null set $E\subseteq \mathbb{R}$ has Lebesgue outer measure zero. Equivalently, for every $ϵ>0$ it can be covered by countably many open intervals whose total length is less than $ϵ$. This definition also applies before assuming $E$ measurable; every such set is Lebesgue measurable with measure zero.