Axiom:Sigma-Algebra Axioms

Definition
Let $X$ be a set.

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

Formulation 1
$\Sigma$ is said to satisfy the sigma-algebra axioms with the following axioms are satisfied:

Formulation 2
$\Sigma$ is said to satisfy the sigma-algebra axioms with the following axioms are satisfied:

Also see

 * Sigma-algebra
 * Equivalence of Definitions of Sigma-Algebra