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Field of sets

From Encyclopedia of Mathematics
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A collection of subsets of a set satisfying:

i) implies ;

ii) implies , .

A -field of sets is a field of sets satisfying in addition

a) , , implies , .

A -field is also sometimes called a Borel field of sets.

Sometimes, an algebra (respectively, a -algebra) of sets is taken to mean a field (respectively, a -field) of sets.

References

[a1] M. Loeve, "Probability theory" , v. Nostrand (1963) pp. 59 (Edition: Third)
[a2] H. Bauer, "Probability theory and elements of measure theory" , Holt, Rinehart&Winston (1972) pp. 7
How to Cite This Entry:
Field of sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Field_of_sets&oldid=28889
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article