Measure and integration Measures Concept
Sigma-finite measure
Summary
A σ-finite measure is a measure for which the whole space is a countable union of sets of finite measure. Lebesgue measure on is the main example. Many basic theorems, such as the Fubini–Tonelli theorem and the Radon–Nikodym theorem, assume σ-finiteness.
Where this leads
12 pages build on this one.
Further reading
About this page
| Tag | WEBBT18D4X |
|---|---|
| URI | m2://WEBBT18D4X |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A12 |
| Specializes | Measure |
| Same as | |
| Changed | 2 November 2026 |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Used by
- Radon–Nikodym theorem
- S-finite measure
- Lebesgue decomposition theorem
- Product measure
- Riesz–Thorin theorem
- Radon–Nikodym derivative
- Hahn–Kolmogorov theorem
- Layer cake representation
- Duality of Lp spaces
- Dual of Lp
- Carathéodory's extension theorem
- Marcinkiewicz interpolation theorem