Definition:Sigma-Ring/Definition 2

From ProofWiki
Jump to navigation Jump to search

Definition

A $\sigma$-ring $\Sigma$ is a system of sets with the following properties:

\((\text {SR} 1)\)   $:$   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:      \(\ds \forall A_n \in \Sigma: n = 1, 2, \ldots:\) \(\ds \bigcup_{n \mathop = 1}^\infty A_n \in \Sigma \)             


Also see


Linguistic Note

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.


Sources