Definition:Sigma-Ring/Definition 2

Definition

$\Sigma$ is a $\sigma$-ring if and only if $\Sigma$ satisfies the $\sigma$-ring axioms:

$(\text {SR} 1)$	$:$	Empty Set:		$\ds \O \in \Sigma $
$(\text {SR} 2)$	$:$	Closure under Set Difference:	$\ds \forall A, B \in \Sigma:$	$\ds A \setminus B \in \Sigma $
$(\text {SR} 3)$	$:$	Closure under Countable Unions:	$\ds \forall A_n \in \Sigma: n = 1, 2, \ldots:$	$\ds \bigcup_{n \mathop = 1}^\infty A_n \in \Sigma $

The $\sigma$ in $\sigma$-ring is the Greek letter sigma which equates to the letter s.

$\sigma$ stands for for somme, which is French for union.

1970: Avner Friedman: Foundations of Modern Analysis ... (previous) ... (next): $\S 1.1$: Rings and Algebras: Definition $1.1.2$

\((\text {SR} 1)\)	$:$	Empty Set:		\(\ds \O \in \Sigma \)
\((\text {SR} 2)\)	$:$	Closure under Set Difference:	\(\ds \forall A, B \in \Sigma:\)	\(\ds A \setminus B \in \Sigma \)
\((\text {SR} 3)\)	$:$	Closure under Countable Unions:	\(\ds \forall A_n \in \Sigma: n = 1, 2, \ldots:\)	\(\ds \bigcup_{n \mathop = 1}^\infty A_n \in \Sigma \)