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
26 pages build on this one.
- Radon–Nikodym theorem
- S-finite measure
- Stein interpolation theorem
- Lebesgue decomposition theorem
- Product measure
- Calderón–Zygmund theorem
- Riesz–Thorin theorem
- Hardy–Littlewood maximal inequality
- Entropic uncertainty principle
- Weil's converse to Haar's theorem
- Radon–Nikodym derivative
- Babenko–Beckner inequality
- Hahn–Kolmogorov theorem
- Layer cake representation
- Hardy–Littlewood–Sobolev inequality
- Hausdorff–Young inequality
- Duality of Lp spaces
- Exponential family
- Dual of Lp
- Carathéodory's extension theorem
- Rubio de Francia extrapolation theorem
- Conservative system
- Marcinkiewicz interpolation theorem
- Muckenhoupt's theorem
- Hellinger distance
- Fisher–Neyman factorization theorem
Further reading
About this page
| Tag | WEBBT18D4X |
|---|---|
| URI | m2://WEBBT18D4X |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A12 |
| Specializes | Measure |
| Same as |
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Used by
- Radon–Nikodym theorem
- S-finite measure
- Lebesgue decomposition theorem
- Product measure
- Riesz–Thorin theorem
- Weil's converse to Haar's theorem
- Radon–Nikodym derivative
- Hahn–Kolmogorov theorem
- Layer cake representation
- Duality of Lp spaces
- Exponential family
- Dual of Lp
- Carathéodory's extension theorem
- Conservative system
- Marcinkiewicz interpolation theorem
- Hellinger distance