## 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