Saturated measure

Short description: Measure in mathematics

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