Saturated measure

In mathematics, a measure is said to be saturated if every locally measurable set is also measurable.^[1] A set ${\displaystyle E}$, not necessarily measurable, is said to be a locally measurable set if for every measurable set ${\displaystyle A}$ of finite measure, ${\displaystyle E\cap A}$ is measurable. ${\displaystyle \sigma }$-finite measures and measures arising as the restriction of outer measures are saturated.

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This page was last edited on 8 January 2024, at 13:11