Measure and integration Set systems Concept
Sigma-algebra
Summary
A σ-algebra on a set is a family of subsets that contains the whole set and is closed under complements and countable unions. In probability theory, the σ-algebra is the family of events, the sets to which we give a probability. The node sigma-algebra gives the precise definition.
Where this leads
12 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Σ-algebra, lead section
About this page
| Tag | 0SV8K0TDGY |
|---|---|
| URI | m2://0SV8K0TDGY |
| Aliases | sigma-field |
| Kind | concept |
| Writing | W1 stated |
| MSC | 28A05 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Special cases
Used by
- Filtration
- Monotone class theorem
- Kolmogorov automorphism
- Regular conditional probability
- Dynkin's π-λ theorem
- Finite-dimensional distributions
- Hahn–Kolmogorov theorem
- Product sigma-algebra
- Carathéodory's extension theorem
- Projection-valued measure
- Lévy's upward theorem