Editing Complete measure (section)

{{Short description|Measure space where every subset of a set with null measure is measurable (and has null measure)}}
{{Refimprove|date=October 2010}}
In [[mathematics]], a '''complete measure''' (or, more precisely, a '''complete measure space''') is a [[measure (mathematics)|measure space]] in which every [[subset]] of every [[null set]] is measurable (having [[measure zero]]). More formally, a measure space (''X'',&nbsp;Σ,&nbsp;''μ'') is complete if and only if<ref>{{Cite book |last=Halmos |first=Paul R. |url=http://link.springer.com/10.1007/978-1-4684-9440-2 |title=Measure Theory |date=1950 |publisher=Springer New York |isbn=978-1-4684-9442-6 |series=Graduate Texts in Mathematics |volume=18 |location=New York, NY |pages=31 |doi=10.1007/978-1-4684-9440-2}}</ref><ref>{{Cite book |last=de Barra |first=G. |url=http://www.sciencedirect.com/science/book/9781904275046 |title=Measure theory and integration |date=2003 |publisher=Woodhead Publishing Limited |isbn=978-1-904275-04-6 |pages=94 |doi=10.1533/9780857099525}}</ref>

:<math>S \subseteq N \in \Sigma \mbox{ and } \mu(N) = 0\ \Rightarrow\ S \in \Sigma.</math>