Editing Measure (mathematics) (section)

===Completeness===
{{Main|Complete measure}}

A measurable set <math>X</math> is called a ''[[null set]]'' if <math>\mu(X) = 0.</math> A subset of a null set is called a ''negligible set''. A negligible set need not be measurable, but every measurable negligible set is automatically a null set. A measure is called ''complete'' if every negligible set is measurable.

A measure can be extended to a complete one by considering the σ-algebra of subsets <math>Y</math> which differ by a negligible set from a measurable set <math>X,</math> that is, such that the [[symmetric difference]] of <math>X</math> and <math>Y</math> is contained in a null set. One defines <math>\mu(Y)</math> to equal <math>\mu(X).</math>