1. Example

2. See also

3. References

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.

Example

is a δ-ring.

It is not a σ-ring since

is not bounded.

See also

• Ring of sets
• Sigma field
• Sigma ring

References

• Cortzen, Allan. "Delta-Ring." From MathWorld—A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/Delta-Ring.html

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