Ring of sets

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A collection of subsets of a set satisfying:

i) implies ;

ii) implies .

It follows that is also closed under finite intersections, since . If , the ring of sets is an algebra of sets.

A -ring of sets is a ring of sets satisfying additionally

a) , , implies .

A -ring is closed under countable intersections. If is a member of a -ring of subsets of , then is a -algebra (cf. Additive class of sets; Algebra of sets).


[a1] H.R. Pitt, "Integration, measure and probability" , Oliver&Boyd (1963) pp. 2–3
How to Cite This Entry:
Ring of sets. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article