Additive Class
Definition of
additive class (completely additive class) 
A class
of subsets of space 
satisfying the following conditions:
Definition of measure space
Consider a space
, the class of subsets 
, and the set function 
. We have
.Borel family of sets
The distance
between two points 
and 
in a Euclidean space 
is
.For any point
in 
and any positive number 
,
is called
-neighbor.The
additive class 
of the entire open set is called Borel family of sets in 
.The combination of space
and 
additive class 
, 
is called Borel space.[0]Top