A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) does not change sign.
The term monotonic may also be used to describe set functions which map subsets of the domain
to non-decreasing values of the codomain. In particular,
if 
is a set function from a collection of sets 
to an ordered set 
, then 
is said to be monotone if whenever 
as elements of 
, 
. This particular definition comes up frequently
in measure theory where many of the families of
functions defined (including outer measure, premeasure,
and measure) begin by considering monotonic set functions.
