Saturated measure

{{Short description|Measure in mathematics}}

In mathematics, a measure is said to be saturated if every locally measurable set is also measurable.Bogachev, Vladmir (2007). Measure Theory Volume 2. Springer. {{isbn|978-3-540-34513-8}}. A set $E$, not necessarily measurable, is said to be a {{visible anchor|locally measurable set}} if for every measurable set $A$ of finite measure, $E\; \backslash cap\; A$ is measurable. $\backslash sigma$-finite measures and measures arising as the restriction of outer measures are saturated.