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

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

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if ${A}_{i}\in \mathcal{S}$ for $i=1,2\mathrm{\dots},$ then ${\cup}_{i=1}^{\mathrm{\infty}}{A}_{i}\in \mathcal{S}$
A $\sigma $ring is also closed under countable^{} intersections^{} since
$${\cap}_{i=1}^{\mathrm{\infty}}{A}_{i}=A{\cup}_{i=1}^{\mathrm{\infty}}(A{A}_{i})$$ 
where $A={\cup}_{i=1}^{\mathrm{\infty}}{A}_{i}$.
$\sigma $rings are used in measure theory.
Title  sigma–ring of sets 

Canonical name  SigmaringOfSets 
Date of creation  20130322 17:04:34 
Last modified on  20130322 17:04:34 
Owner  Mathprof (13753) 
Last modified by  Mathprof (13753) 
Numerical id  7 
Author  Mathprof (13753) 
Entry type  Definition 
Classification  msc 28A05 