| context | $X $ |
| definiendum | $ \langle X,\Sigma,\mu\rangle $ … complete measure space over $X$ |
| postulate | $ \langle X,\Sigma,\mu\rangle $ … measure space |
| $\mu(N)=0$ |
| $N'\subseteq N $ |
| postulate | $ N'\in\Sigma $ |
In a complete measure space, subsets of null-sets can also be measured (and they then have zero measure as well). This notion is just introduced to prevent some pathologies.
Wikipedia: Complete measure