The term "intensity function" has at least two distinct definitions related to the theory of point processes.
In some literature, the intensity 
of a stationary
point process 
is defined to be the quantity
![lambda=lim_(hv0)(Pr{N(0,h]>0})/h](/images/equations/IntensityFunction/NumberedEquation1.svg) |
(1)
|
provided it exists. Here, 
denotes probability. In particular,
it makes sense to talk about point processes having
infinite intensity, though when finite, 
allows 
to be rewritten so that
![Pr{N(x,x+h]>0}=lambdah+o(h)](/images/equations/IntensityFunction/NumberedEquation2.svg) |
(2)
|
as 
where here, 
denotes little-O notation (Daley and Vere-Jones
2007).
Other authors define the function 
to be an intensity function of a point
process 
provided that 
is a density of the intensity measure 
associated to 
relative to Lebesgue measure,
i.e., if for all Borel sets 
in 
,
 |
(3)
|
where 
is the spatial integration variable
and 
denotes Lebesgue measure (Pawlas 2008).
