(Complete measure space) The measure space is "complete" if contains all subsets of sets of measure zero.

(Saturated measure space) The measure space is "saturated" if every locally measurable set is measurable.

(Completion of measure via addition of null sets) For a measure space there is a complete measure space such that

1. ,

2. .

3. where and ,

The rule 3 defines a -algebra. The extends to such -algebra without ambiguity.