complete measure (original) (raw)

If a measure space is not complete, there exists a completion (http://planetmath.org/CompletionOfAMeasureSpace) of it, which is a complete measure space (X,𝒮¯,μ¯) such that 𝒮⊂𝒮¯ and μ¯|𝒮=μ, where 𝒮¯ is the smallest σ-algebra containing both 𝒮 and all subsets of elements of zero measure of 𝒮.