Additive class of sets

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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.


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