μ-completion
（ plural ）
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(mathematical analysis) A σ-algebra which is obtained as a completion
of a given σ-algebra, which includes all subsets of the given measure space which simultaneously contain a member of the given σ-algebra and are contained by a member of the given σ-algebra, as long as the contained and containing measurable sets have the same measure, in which case the subset in question is assigned a measure equal to the common measure of its contained and containing measurable sets (so the measure is also being completed, in parallel with the σ-algebra).
μ-completion
When constructing the μ-completion of the measurable space, we adjoin all subsets that lie between two measurable sets of equal measure so that the measure becomes complete as well.
When constructing the μ-completion of the measurable space, we adjoin all subsets that lie between two measurable sets of equal measure so that the measure becomes complete as well.
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