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==Definition==
Given a system of sets, {{M|S}}, the ''hereditary {{sigma|ring}} generated by {{M|S}}'' is{{rMTH}}:
* The smallest ''[[hereditary]]'' [[sigma-ring|{{sigma|ring}}]] containing {{M|S}}
We denote this {{M|\mathcal{H}_{\sigma R}(S)}}<ref group="Note">If {{M|\mathcal{H}(A)}} denotes the [[hereditary system of sets]] generated by {{M|A}} and {{M|\sigma_R(B)}} the [[sigma-ring]] generated by {{M|B}}, then we have {{M|1=\mathcal{H}(\sigma_R(A))=\sigma_R(\mathcal{H}(A))}}</ref>
==Claims==
* {{M|1=\mathcal{H}(\sigma_R(S))=\sigma_R(\mathcal{H}(S))}} - see [[Notes:Hereditary sigma-ring]]
==See also==
* [[Hereditary system generated by]]
==Notes==
<references group="Note"/>
==References==
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