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 R[1] of sets such that:
- ∀A∈R∀B∈R(A∪B∈R)
- ∀A∈R∀B∈R(E−F∈R)
First theorems
[Expand]
The empty set belongs to every ring
References
- Jump up ↑ Page 19 - Halmos - Measure Theory - Springer - Graduate Texts in Mathematics (18)
