Word.ws English Dictionary

μ-completion

μ-completion noun: 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).

Noun

μ-completion (plural μ-completions)

  1. 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).
    • Every σ-algebra has a μ-completion: if a σ-algebra is complete, then it is equal to its μ-completion, otherwise it is contained by its μ-completion.

Forms of μ-completion

pluralμ-completions

Questions about μ-completion

What does μ-completion mean?
Μ-completion means 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).
What part of speech is μ-completion?
Μ-completion is a noun.
What is the plural of μ-completion?
The plural of μ-completion is μ-completions.

Words near μ-completion in the dictionary

  1. λ/4 plates
  2. ΛCDM
  3. λmax
  4. λmaxes
  5. μ-
  6. μ-completion
  7. μ-completions
  8. μ-oxido dihydrogen
  9. μ-PD
  10. μ-scope
  11. μ-scopes

Source and license

Adapted from Wiktionary: μ-completion (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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