Saturated measure

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

References

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