Measure and integration Measurable functions Concept
Measurable function
Summary
A measurable function is a map between measurable spaces under which the preimage of every measurable set is measurable. These are the functions that one can integrate in Lebesgue's theory, and in probability they are the random variables. Sums, products, limits and suprema of sequences of real measurable functions are again measurable.
Where this leads
38 pages build on this one.
- Pettis measurability theorem
- Radon–Nikodym theorem
- Measure-preserving transformation
- Slowly varying function
- Scheffé's lemma
- Regular variation
- Egorov's theorem
- Lp space
- L-infinity space
- Weak Lp space
- Choquet integral
- Bartle–Dunford–Schwartz integral
- Lorentz space
- Convergence in measure
- Dominated convergence theorem
- Vitali convergence theorem
- Quasi-measure-preserving map
- Littlewood's three principles
- Radon–Nikodym derivative
- Monotone convergence theorem
- Integral of a non-negative function
- Lusin's theorem
- Prékopa–Leindler inequality
- Riesz's subsequence theorem
- Young measure
- Product sigma-algebra
- Disintegration theorem
- Distribution function of a measurable function
- Simple function
- Coarea formula
- Integrable function
- Fatou's lemma
- Markov kernel
- Measure with density
- Orlicz space
- Pushforward measure
- Essential supremum
- Absolute continuity of the Lebesgue integral
Further reading
About this page
| Tag | YYNCJSR0PJ |
|---|---|
| URI | m2://YYNCJSR0PJ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A20 |
| Same as | |
| Changed | 2 November 2026 |
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What links here
Used by
- Pettis measurability theorem
- Radon–Nikodym theorem
- Measure-preserving transformation
- Slowly varying function
- Regular variation
- Egorov's theorem
- Lp space
- L-infinity space
- Weak Lp space
- Choquet integral
- Bartle–Dunford–Schwartz integral
- Lorentz space
- Convergence in measure
- Quasi-measure-preserving map
- Littlewood's three principles
- Monotone convergence theorem
- Integral of a non-negative function
- Lusin's theorem
- Prékopa–Leindler inequality
- Young measure
- Product sigma-algebra
- Disintegration theorem
- Distribution function of a measurable function
- Simple function
- Coarea formula
- Integrable function
- Markov kernel
- Measure with density
- Orlicz space
- Pushforward measure
- Essential supremum