Borel set

In mathematics, a Borel set is a set that belongs to the $\sigma -$algebra (see the entry Sigma algebra) generated by the open sets of a topological space.

Formal definition

Let $(X,O)$ be a topological space, i.e. $X$ is a set and $O$ are the open sets of $X$ (or, equivalently, the topology of $X$). Then $A\subset X$ is a Borel set of $X$ if $A\in \sigma (O)$, where $\sigma (O)$ denotes the sigma algebra generated by $O$.