# sigma–ring of sets

A $\sigma$-ring of sets is a nonempty collection $\mathcal{S}$ of sets such that

• if $A\in\mathcal{S}$ and $B\in\mathcal{S}$ then $A-B\in\mathcal{S}$ and

• if $A_{i}\in\mathcal{S}$ for $i=1,2\ldots,$ then $\cup_{i=1}^{\infty}A_{i}\in\mathcal{S}$

A $\sigma$-ring is also closed under countable intersections since

 $\cap_{i=1}^{\infty}A_{i}=A-\cup_{i=1}^{\infty}(A-A_{i})$

where $A=\cup_{i=1}^{\infty}A_{i}$.

$\sigma$-rings are used in measure theory.

Title sigma–ring of sets SigmaringOfSets 2013-03-22 17:04:34 2013-03-22 17:04:34 Mathprof (13753) Mathprof (13753) 7 Mathprof (13753) Definition msc 28A05