Ring of sets
From Encyclopedia of Mathematics
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).
References
[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: http://encyclopediaofmath.org/index.php?title=Ring_of_sets&oldid=14767
Ring of sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ring_of_sets&oldid=14767
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article