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.