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.

References

1. Bogachev, Vladmir (2007). Measure Theory Volume 2. Springer. ISBN 978-3-540-34513-8.