Axiom:Sigma-Algebra Axioms/Formulation 2

Let $X$ be a set.

Let $\Sigma$ be a system of subsets over $X$.

$\Sigma$ is a $\sigma$-algebra over $X$ the following axioms are satisfied:

These criteria are called the $\sigma$-algebra axioms.

Also see

 * Axiom:Sigma-Algebra Axioms/Formulation 1 for an alternative formulation of the $\sigma$-algebra axioms


 * Sigma-algebra