Countable additivity is the property of a set function 
that, for every countable disjoint collection of sets 
on which 
is defined,
 |
A function having countable additivity is said to be countably additive.
Countably additive functions are countably subadditive by definition. Moreover, provided that 
where 
is the empty set, every
countably additive function 
is necessarily finitely
additive.
