# Additive class of sets

From Encyclopedia of Mathematics

A collection of subsets of a set satisfying:

i) ;

ii) implies ;

iii) implies .

The collection is a completely additive class of sets if it satisfies:

a) ;

b) implies ;

c) , , implies .

A completely additive class is also called a -field, a -algebra or a Borel field of sets.

#### References

[a1] | M.E. Munroe, "Measure and integration" , Addison-Wesley (1953) pp. 60 |

**How to Cite This Entry:**

Additive class of sets.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Additive_class_of_sets&oldid=28040

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