Abstract
The measure λ and its measure space are complete if subsets of λ null sets in S are also in S; if so, the subsets are λ null. According to the following theorem, if (S, S,λ) is not complete it can be completed, that is, S can be enlarged to obtain a complete measure space.
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© 1994 Springer Science+Business Media New York
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Doob, J.L. (1994). Measure Spaces. In: Measure Theory. Graduate Texts in Mathematics, vol 143. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0877-8_5
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DOI: https://doi.org/10.1007/978-1-4612-0877-8_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6931-1
Online ISBN: 978-1-4612-0877-8
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