In mathematics, a nonempty collection of sets is called a δ-ring (pronounced delta-ring) if it is closed under union, relative complementation, and countable intersection:
- if for all
If only the first two properties are satisfied, then 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.