# Sigma-ring

From Maths

A **Sigma-ring** or [math]\sigma[/math]-ring, is closely related to rings of sets, and just like algebras of sets are related to rings of sets, so is [math]\sigma[/math]-ring to [math]\sigma[/math]-algebra

## Definition

A non-empty class of sets [ilmath]S[/ilmath] is a [ilmath]\sigma[/ilmath]-ring if^{[1]}:

- for [ilmath]A\in S[/ilmath] and [ilmath]B\in S[/ilmath] then [ilmath]A-B\in S[/ilmath]
- If [math]\{A_n\}_{n=1}^\infty\subset S[/math] then [math]\cup^\infty_{n=1}A_n\in S[/math]

That is to say it is closed under subtraction and countable union

## References

- ↑ Measure Theory, p24 - Halmos - Graduate Texts in Mathematics (18) - Springer