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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:

  1. if
  2. if
  3. 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.

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