tags:definition |analysis

Borel Sigma Algebra

Statements

Definition. (@Sal08, Example B.1, @Hun11) Let $(X,\tau )$ be a topological space. The Borel sigma algebra $\mathfrak{B}$ on $X$ is the sigma algebra generated by the open sets of $\tau$. The elements of $\mathfrak{B}$ are said to be Borel sets.

Remark. A Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable countable intersection, and relative complement.