Measure and integration Measures Concept
Measure space
Summary
A measure space is a set together with a σ-algebra of subsets and a measure on that σ-algebra. It is the basic object of measure theory and of the Lebesgue integral. A probability space is a measure space of total measure .
Where this leads
35 pages build on this one.
- Clarkson's inequalities
- Radon–Nikodym theorem
- Measure-preserving transformation
- Restriction of a measure
- Finite measure
- Pettis integral
- Null set
- Almost everywhere
- Egorov's theorem
- Lp space
- L-infinity space
- Weak Lp space
- Density of simple functions in Lp
- Lorentz space
- Convergence in measure
- Loeb measure
- Sigma-finite measure
- Quasi-measure-preserving map
- Complete measure
- Radon–Nikodym derivative
- Inner measure
- Bochner integral
- Integral of a non-negative function
- Continuity of measure from below and above
- Sierpiński's theorem on non-atomic measures
- Riesz's subsequence theorem
- Duality of Lp spaces
- Distribution function of a measurable function
- Integrable function
- Measure with density
- Riesz–Fischer theorem
- Non-atomic measure
- Orlicz space
- Essential supremum
- Completion of a measure
Further reading
About this page
| Tag | P15VQS5DJ9 |
|---|---|
| URI | m2://P15VQS5DJ9 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A12 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Clarkson's inequalities
- Radon–Nikodym theorem
- Measure-preserving transformation
- Restriction of a measure
- Finite measure
- Pettis integral
- Null set
- Almost everywhere
- Egorov's theorem
- Lp space
- L-infinity space
- Weak Lp space
- Density of simple functions in Lp
- Lorentz space
- Convergence in measure
- Loeb measure
- Sigma-finite measure
- Quasi-measure-preserving map
- Complete measure
- Inner measure
- Bochner integral
- Integral of a non-negative function
- Continuity of measure from below and above
- Sierpiński's theorem on non-atomic measures
- Duality of Lp spaces
- Distribution function of a measurable function
- Integrable function
- Measure with density
- Riesz–Fischer theorem
- Non-atomic measure
- Orlicz space
- Essential supremum
- Completion of a measure