# Definition:Sigma-Algebra/Definition 4

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## 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

## 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**.