Borel $\sigma$-algebra

For any topological space $X$, the Borel sigma algebra of $X$ is the $\sigma$–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 $\sigma$-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 $\sigma$ algebra
Synonym	Borel sigma algebra
Related topic	SigmaAlgebra
Related topic	OuterRegular
Related topic	LebesgueMeasure
Defines	Borel subset
Defines	Borel set