Countable monotonicity is a property of a nonnegative set function. Let 
be a set and 
a collection of subsets of 
. A set function ![mu:S->[0,infty]](/images/equations/CountableMonotonicity/Inline4.svg)
has countable monotonicity
if, whenever a set 
and a countable collection
of sets in 
satisfy 
,
 |
A set function with this property is said to be countably monotone.
If 
is a sigma-algebra, then any nonnegative set function 
that is monotone and
countably additive is countably monotone.
Here monotone means that 
whenever 
for 
. The converse is not true in general.
