A multidimensional point process is a measurable function from a probability space 
into 
where 
is the set of all finite
or countable subsets
of 
having no accumulation point in 
and where 
is the sigma-algebra
generated over 
by the sets
 |
for all bounded Borel subsets 
and every nonnegative
integer 
. Here, 
denotes the cardinality
or order of the set 
.
A multidimensional point process is sometimes abbreviated MPP, though care should be exhibited not to confuse the notion with that of a marked point process.
Despite a number of apparent differences, one can show that multidimensional point processes are a special case of a random closed set
on 
(Baudin 1984).
