Measure and integration Set systems Concept
Measurable space
Summary
A measurable space is a set together with a σ-algebra of its subsets. The sets in the σ-algebra are the measurable sets. Measurable spaces are the setting in which measures, measurable functions and random variables are defined.
Where this leads
22 pages build on this one.
- Non-measurable set
- Absolutely continuous measure
- Hahn decomposition theorem
- S-finite measure
- Measure space
- Strongly measurable function
- Universally measurable set
- Measure
- Ionescu-Tulcea theorem
- Choquet integral
- Signed measure
- Set-valued measure
- Standard Borel space
- Nikodym convergence theorem
- Product sigma-algebra
- Measurable function
- Mutually singular measures
- Simple function
- Markov kernel
- Jordan decomposition of a signed measure
- Complex measure
- Pushforward measure
Further reading
About this page
| Tag | N4KDT83V3S |
|---|---|
| URI | m2://N4KDT83V3S |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A05 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Non-measurable set
- Absolutely continuous measure
- Hahn decomposition theorem
- S-finite measure
- Measure space
- Strongly measurable function
- Universally measurable set
- Measure
- Ionescu-Tulcea theorem
- Choquet integral
- Signed measure
- Set-valued measure
- Standard Borel space
- Nikodym convergence theorem
- Product sigma-algebra
- Measurable function
- Mutually singular measures
- Simple function
- Markov kernel
- Complex measure
- Pushforward measure