borel_sigma-algebra

Definition

The $\sigma$-algebra $\sigma\left. \left( \mathcal{O} \right) \right.$ generated by the open sets $\mathcal{O} = \mathcal{O}_{\mathbb{R}^{n}}$ of $\mathbb{R}^{n}$ is called a $\sigma$-algebra, and its members are called Borel sets or Borel measurable sets. We write $\mathcal{B}\left. \left( \mathbb{R}^{n} \right) \right.$ for the Borel sets in $\mathbb{R}^{n}$.