Saturated measure
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Short description: Measure in mathematics
In mathematics, a measure is said to be saturated if every locally measurable set is also measurable.[1] 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.
References
- ↑ Bogachev, Vladmir (2007). Measure Theory Volume 2. Springer. ISBN 978-3-540-34513-8.
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