The term "null set" is sometimes also used to refer to the empty set; see that article. Alternatively, it may be used for any notion of negligible set; see that article.
Which sets are null will depend on the measure considered. Thus one may speak of mnull sets for a given measure m.

Let X be a measurable space, let m be a measure on X, and let N be a measurable set[?] in X. If m is a positive measure[?], then N is null if its measure m(N) is zero. If m is not a positive measure, then N is mnull if N is mnull, where m is the total variation[?] of m; this is stronger than simply saying that m(N) = 0.
A nonmeasurable set is considered null if it's a subset of a null measurable set. Some references require a null set to be measurable; however, subsets of null sets are still negligible for measuretheoretic purposes.
When talking about null sets in Euclidean nspace R^{n}, it is usually understood that the measure being used is Lebesgue measure.
The empty set is always a null set. More generally, any countable union of null sets is null. Any subset of a null set is itself a null set. Together, these facts show that the mnull sets of X form a sigmaideal[?] on X. Similarly, the measurable mnull sets form a sigmaideal of the sigmaalgebra of measurable sets. Thus, null sets may be interpreted as negligible sets, defining a notion of almost everywhere.
For Lebesgue measure on R^{n}, all 1point sets are null, and therefore all countable sets are null. In particular, the set Q of rational numbers is a null set, despite being dense in R. The Cantor set is an example of an uncountable null set in R.
More generally, a subset N of R is null if and only if:
Null sets play a key role in the definition of the Lebesgue integral: if functions f and g are equal except on a null set, then f is integrable if and only if g is, and their integrals are equal.
A measure in which all null sets are measurable is complete. Any noncomplete measure can be completed to form a complete measure, by assuming that null sets have measure zero. Lebesgue measure is an example of a complete measure; in some constructions, it's defined as the completion of a noncomplete Borel measure.
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