# Definition:Extended Real Sigma-Algebra

## Definition

Let $\left({\overline{\R}, \tau}\right)$ be the extended real number space.

The extended real $\sigma$-algebra $\overline{\mathcal B}$ is the Borel $\sigma$-algebra $\mathcal B \left({\overline{\R}, \tau}\right)$.

## Also known as

As usual, one may also write sigma-algebra instead of $\sigma$-algebra.