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Delta-ring : ウィキペディア英語版
Delta-ring
In mathematics, a nonempty collection of sets \mathcal is called a δ-ring (pronounced ''delta-ring'') if it is closed under union, relative complementation, and countable intersection:
#A \cup B \in \mathcal if A, B \in \mathcal
#A - B \in \mathcal if A, B \in \mathcal
#\bigcap_^ A_ \in \mathcal if A_ \in \mathcal for all n \in \mathbb
If only the first two properties are satisfied, then \mathcal 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.
== See also ==

*Ring of sets
*Sigma field
*Sigma ring

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Delta-ring」の詳細全文を読む



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