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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
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.