Definition:Sigma-Algebra/Definition 1

Definition
Let $X$ be a set.

A $\sigma$-algebra $\mathcal R$ over $X$ is a system of subsets of $X$ with the following properties:

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.