# μ-completion

*Noun.*(

*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).

This is an unmodified, but possibly outdated, definition from Wiktionary and used here under the Creative Commons license. Wiktionary is a great resource. If you like it too, please donate to Wikimedia.

This entry was last updated on RefTopia from its source on 3/20/2012.