Definition:Sigma-Algebra/Definition 3

Definition

A $\sigma$-algebra $\Sigma$ is a $\sigma$-ring with a unit.

Also known as

The term sigma-algebra can also be seen without the hyphen: sigma algebra.

Some sources refer to a sigma-algebra as a sigma-field

Also see

• Equivalence of Definitions of Sigma-Algebra

Linguistic Note

The $\sigma$ in $\sigma$-algebra is the Greek letter sigma which equates to the letter s.

$\sigma$ stands for for somme, which is French for union, and also summe, which is German for union.

Sources

• 1970: Avner Friedman: Foundations of Modern Analysis ... (previous) ... (next): $\S 1.1$: Rings and Algebras