Borel σ-algebra
For any topological space
X, the Borel sigma algebra of X is the σ–algebra ℬ generated by the open sets of X. In other words, the Borel sigma algebra is equal to the intersection of all sigma algebras 𝒜 of X having the property that every open set of X is an element of 𝒜.
An element of ℬ is called a Borel subset of X, or a Borel set.
| Title | Borel σ-algebra |
|---|---|
| Canonical name | Borelsigmaalgebra |
| Date of creation | 2013-03-22 12:00:31 |
| Last modified on | 2013-03-22 12:00:31 |
| Owner | djao (24) |
| Last modified by | djao (24) |
| Numerical id | 10 |
| Author | djao (24) |
| Entry type | Definition |
| Classification | msc 28A05 |
| Synonym | Borel σ algebra |
| Synonym | Borel sigma algebra |
| Related topic | SigmaAlgebra |
| Related topic | OuterRegular |
| Related topic | LebesgueMeasure |
| Defines | Borel subset |
| Defines | Borel set |