In mathematics, a non-empty collection of sets \mathcal{R} is called a -ring (pronounced "") if it is closed under union, relative complementation, and countable intersection. The name "delta-ring" originates from the German word for intersection, "Durschnitt", which is meant to highlight the ring's closure under countable intersection, in contrast to a 𝜎-ring which is closed under countable unions.

Definition

A family of sets \mathcal{R} is called a -ring if it has all of the following properties: If only the first two properties are satisfied, then \mathcal{R} is a ring of sets but not a -ring. Every 𝜎-ring is a -ring, but not every -ring is a 𝜎-ring. -rings can be used instead of σ-algebras in the development of measure theory if one does not wish to allow sets of infinite measure.

Examples

The family is a -ring but not a 𝜎-ring because is not bounded.