# Field of sets

From Encyclopedia of Mathematics

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=14393

This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article