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

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