Delta ring

In mathematics, a nonempty collection of sets R is called a δ-ring (pronounced delta-ring) if it is closed under union, relative complementation, and countable intersection:

1. A ∪ B ∈ R if A , B ∈ R
2. A − B ∈ R if A , B ∈ R
3. ⋂ n = 1 ∞ A n ∈ R if A n ∈ R for all n ∈ N

If only the first two properties are satisfied, then R is a ring but not a δ-ring. Every σ-ring is a δ-ring, but not every δ-ring is a σ-ring.

δ-rings can be used instead of σ-fields in the development of measure theory if one does not wish to allow sets of infinite measure.