Let 
be a set and 
a collection of subsets of 
. A set function ![mu:S->[0,infty]](/images/equations/CountableMonotonicity/Inline4.svg)
is said to possess countable monotonicity
provided that, whenever a set 
is covered by a countable
collection 
of sets in 
,
 |
A function which possesses countable monotonicity is said to be countably monotone.
One can easily verify that any set function 
which is both monotone
(in the sense of mapping subsets of the domain to subsets of the range) and countably
additive is necessarily countably monotone. The converse is not true in general.
