Additive class of sets
From Encyclopedia of Mathematics
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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.
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
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