"μ-completion" meaning in All languages combined

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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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          "text": "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.",
          "type": "example"
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      ],
      "glosses": [
        "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)."
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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)."
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      "related": [
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  "word": "μ-completion"
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  "pos": "noun",
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          "text": "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.",
          "type": "example"
        }
      ],
      "glosses": [
        "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)."
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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)."
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  "word": "μ-completion"
}