μcompletion
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EnglishEdit
NounEdit
μcompletion (plural μcompletions)
 (analysis) A σalgebra which is obtained as a "completion" of a given σalgebra, which includes all subsets of the given measure space which simultaneously contain a member of the given σalgebra and are contained by a member of the given σalgebra, 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 σalgebra).

Every σalgebra has a μcompletion: if a σalgebra is complete, then it is equal to its μcompletion, otherwise it is contained by its μcompletion.
