Definition: Ring of Sets (measure-theoretic definition)

Let \(M\) be a set and let \({\mathcal {R}}\) be a system of its subsets \({\mathcal {R}}\) is called a ring of sets, if is is closed under set-theoretic differences and set-theoretic unions, i.e. if

\[S,T\in {\mathcal {R}}\Longrightarrow \cases{S\setminus T\in {\mathcal {R}},\\S\cup T\in {\mathcal {R}}.}\]

Please note that in particular \(\emptyset \in {\mathcal {R}}\), if we take \(S=T\).

Definitions: 1 2 3

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Adapted from CC BY-SA 3.0 Sources:

  1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück