In mathematics, a measure is said to be saturated if every locally measurable set is also measurable. A set E {\displaystyle E} , not necessarily measurable, is said to be a locally measurable set if for every measurable set A {\displaystyle A} of finite measure, E ∩ A {\displaystyle E\cap A} is measurable. σ {\displaystyle \sigma } -finite measures and measures arising as the restriction of outer measures are saturated.
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