Borel σ-algebra

For any topological spaceMathworldPlanetmath X, the Borel sigma algebra of X is the σ–algebra 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 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