Definition:Extended Real Sigma-Algebra

Definition

Let $\struct {\overline \R, \tau}$ be the extended real number space.

The extended real $\sigma$-algebra $\overline \BB$ is the Borel $\sigma$-algebra $\map \BB {\overline \R, \tau}$.

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 $\overline \BB$ from $\map \BB \R$
• Extended Real Sigma-Algebra Induces Borel Sigma-Algebra on Reals
• Generators for Extended Real Sigma-Algebra, giving generators for $\overline \BB$

Sources

• 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $\S 8$