Complete measure

In mathematics, a complete measure (or, more precisely, a complete measure space) is a measure space in which every subset of every null set is measurable (having measure zero). More formally, a measure space (X, Σ, μ) is complete if and only if^[1]^[2]

S\subseteq N\in \Sigma {\mbox{ and }}\mu (N)=0\ \Rightarrow \ S\in \Sigma .

^ Halmos, Paul R. (1950). Measure Theory. Graduate Texts in Mathematics. Vol. 18. New York, NY: Springer New York. p. 31. doi:10.1007/978-1-4684-9440-2. ISBN 978-1-4684-9442-6.
^ de Barra, G. (2003). Measure theory and integration. Woodhead Publishing Limited. p. 94. doi:10.1533/9780857099525. ISBN 978-1-904275-04-6.

[1] Halmos, Paul R. (1950). Measure Theory. Graduate Texts in Mathematics. Vol. 18. New York, NY: Springer New York. p. 31. doi:10.1007/978-1-4684-9440-2. ISBN 978-1-4684-9442-6.

[2] Barra, G. (2003). Measure theory and integration. Woodhead Publishing Limited. p. 94. doi:10.1533/9780857099525. ISBN 978-1-904275-04-6.

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