In mathematics, a

measure Measure may refer to: * Measurement, the assignment of a number to a characteristic of an object or event Law * Ballot measure, proposed legislation in the United States * Church of England Measure, legislation of the Church of England * Mea ...

is said to be saturated if every locally measurable set is also

measurable In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simila ...

.Bogachev, Vladmir (2007). ''Measure Theory Volume 2''. Springer. . A set

E

, not necessarily measurable, is said to be a 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 measure In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer mea ...

s are saturated.

References

Measures (measure theory) {{mathanalysis-stub