Lefschetz zeta function: Difference between revisions
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In [[mathematics]], a [[Measure (mathematics)|measure]] is said to be '''saturated''' if every locally measurable set is also [[measurable]].<ref>Bogachev, Vladmir (2007). ''Measure Theory Volume 2''. Springer. ISBN 978-3-540-34513-8.</ref> A set <math>E</math>, not necessarily measurable, is said to be '''locally measurable''' if for every measurable set <math>A</math> of finite measure, <math>E \cap A</math> is measurable. <math>\sigma</math>-finite measures, and measures arising as the restriction of [[outer measure]]s, are saturated. | |||
==References== | |||
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[[Category:Measures (measure theory)]] | |||
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Revision as of 01:50, 30 April 2013
In mathematics, a measure is said to be saturated if every locally measurable set is also measurable.[1] A set , not necessarily measurable, is said to be locally measurable if for every measurable set of finite measure, is measurable. -finite measures, and measures arising as the restriction of outer measures, are saturated.
References
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- ↑ Bogachev, Vladmir (2007). Measure Theory Volume 2. Springer. ISBN 978-3-540-34513-8.