Ring of sets
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A Ring of sets is also known as a Boolean ring
Note that every Algebra of sets is also a ring, and that an Algebra of sets is sometimes called a Boolean algebra
Definition
A Ring of sets is a non-empty class [ilmath]R[/ilmath][1] of sets such that:
- [math]\forall A\in R\forall B\in R(A\cup B\in R)[/math]
- [math]\forall A\in R\forall B\in R(E-F\in R)[/math]
First theorems
The empty set belongs to every ring
Take any [math]A\in R[/math] then [math]A-A\in R[/math] but [math]A-A=\emptyset[/math] so [math]\emptyset\in R[/math]
References
- ↑ Page 19 - Halmos - Measure Theory - Springer - Graduate Texts in Mathematics (18)
