Definition:Sigma-Algebra/Definition 4

Definition

Let $X$ be a set.

A $\sigma$-algebra $\Sigma$ over $X$ is an algebra of sets which is closed under countable unions.

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.