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.

Also see

 * Characterization of Extended Real Sigma-Algebra, showing an explicit construction of $\overline{\mathcal B}$ from $\mathcal B \left({\R}\right)$
 * Extended Real Sigma-Algebra Induces Borel Sigma-Algebra on Reals
 * Generators for Extended Real Sigma-Algebra, giving generators for $\overline{\mathcal B}$