## Complete measure space

### Set

 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 $N'\in\Sigma$

### Discussion

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.

### Reference

Wikipedia: Complete measure