Countable additivity is the property of a set function 
that, for every countable collection of pairwise disjoint
sets 
on which 
is defined and whose union is also in its domain,
 |
A set function having countable additivity is said to be countably additive.
A nonnegative countably additive set function on a sigma-algebra is countably
subadditive. Moreover, provided that 
, where 
is the empty set, every
countably additive set function 
is finitely additive.
