In mathematics, there are two different notions of a ring of sets, both referring to certain families of sets. In order theory, a nonempty family of sets is called a ring (of sets) if it is closed under intersection and union. That is, for any ,
- and
In measure theory, a ring of sets is instead a family closed under unions and set-theoretic differences. That is, it obeys the two properties
- and
This implies that it is also closed under intersections, because of the identity
however, a family of sets that is closed under unions and intersections might not be closed under differences.
Read more about Ring Of Sets: Examples, Related Structures
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