In mathematics, a measure is said to be saturated if every locally measurable set is also measurable.[1] A set đ {\displaystyle E}
, not necessarily measurable, is said to be a locally measurable set if for every measurable set đ {\displaystyle A}
of finite measure, đ {\displaystyle E\cap A}
is measurable. đ {\displaystyle \sigma }
-finite measures and measures arising as the restriction of outer measures are saturated.
References
[edit]- ^ Bogachev, Vladmir (2007). Measure Theory Volume 2. Springer. ISBN 978-3-540-34513-8.
