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
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