Null Set of a Measure

Let $(X,\mathcal{F},\mu)$ be a measure space. A subset $N$ of $X$ is $\mu$-null, or a null set for $\mu$, if there is a measurable set $B\in\mathcal{F}$ with $N\subseteq B$ and $\mu(B)=0$. A null set is not required to belong to $\mathcal{F}$.