Borel $\sigma$-algebra BorelSigmaAlgebra 2001-11-17 10:53:44 2006-11-30 19:51:26 Definition Borel subset Borel set \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} For any topological space $X$, the \emph{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 \emph{Borel subset} of $X$, or a \emph{Borel set}.