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Borel $\sigma$-algebra (Definition)

For any topological space $ X$, the Borel sigma algebra of $ X$ is the $ \sigma$-algebra $ \mathcal{B}$ generated by the open sets of $ X$. In other words, the Borel sigma algebra is equal to the intersection of all sigma algebras $ \mathcal{A}$ of $ X$ having the property that every open set of $ X$ is an element of $ \mathcal{A}$.

An element of $ \mathcal{B}$ is called a Borel subset of $ X$, or a Borel set.



"Borel $\sigma$-algebra" is owned by djao. [ full author list (2) | owner history (1) ]
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See Also: $\sigma$-algebra, outer regular, Lebesgue measure

Other names:  Borel $\sigma$ algebra, Borel sigma algebra
Also defines:  Borel subset, Borel set
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Cross-references: property, sigma algebras, intersection, open sets, generated by, topological space
There are 19 references to this entry.

This is version 6 of Borel $\sigma$-algebra, born on 2001-11-17, modified 2006-11-30.
Object id is 951, canonical name is BorelSigmaAlgebra.
Accessed 19614 times total.

Classification:
AMS MSC: 28A05 (Measure and integration :: Classical measure theory :: Classes of sets , measurable sets, Suslin sets, analytic sets)
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