Delta-ring
In mathematics, a non-empty collection of sets is called a δ-ring (pronounced delta-ring) if it is closed under union, relative complementation, and countable intersection:
- for all
- for all
- 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.
gollark: ρυστ
gollark: LOSEinux.
gollark: See? Hackerman is set in a utopian future when GUUT has taken over.
gollark: It'll have to sync with others somehow.
gollark: Yep!
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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