View source for Sigma-ring

A '''Sigma-ring''' or <math>\sigma</math>-ring, is closely related to [[Ring of sets|rings of sets]], and just like [[Algebra of sets|algebras of sets]] are related to rings of sets, so is <math>\sigma</math>-ring to [[Sigma-algebra|<math>\sigma</math>-algebra]]

==Definition==
A non-empty class of sets {{M|S}} is a {{sigma|ring}} if<ref>Measure Theory, p24 - Halmos - Graduate Texts in Mathematics (18) - Springer</ref>:
* for {{M|A\in S}} and {{M|B\in S}} then {{M|A-B\in S}}
* 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 [[Set subtraction|subtraction]] and [[Countable|countable]] [[Union|union]]

{{Definition|Measure Theory}}
==References==