Measure and integration Measures Concept
Null set
Summary
A null set in a measure space is a measurable set of measure zero. Null sets are the sets that measure theory can ignore: changing a function on a null set does not change its integral. For Lebesgue measure, every countable set is null, and so is the Cantor set.
Where this leads
14 pages build on this one.
- Absolutely continuous measure
- Standard probability space
- Kahane–Katznelson theorem
- Almost everywhere
- Contiguity of measures
- Quasi-ergodicity
- Menshov's set of multiplicity of measure zero
- Quasi-measure-preserving map
- Complete measure
- Quasi-invariant measure
- Parametric transversality theorem
- Isomorphism theorem for measure algebras
- Essential supremum
- Completion of a measure
Further reading
About this page
| Tag | VQQM4Y550T |
|---|---|
| URI | m2://VQQM4Y550T |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A12, 28A05 |
| Same as |
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Used by
- Absolutely continuous measure
- Standard probability space
- Kahane–Katznelson theorem
- Almost everywhere
- Quasi-ergodicity
- Menshov's set of multiplicity of measure zero
- Quasi-measure-preserving map
- Complete measure
- Quasi-invariant measure
- Parametric transversality theorem
- Isomorphism theorem for measure algebras
- Essential supremum
- Completion of a measure