Field of sets

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


M. Hazewinkel


This text originally appeared in Encyclopaedia of Mathematics - ISBN 1402006098

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