A multidimensional point process is a measurable function from a probability space into where is the set of all finite or countable subsets of not containing an accumulation point and where is the sigma-algebra generated over by the sets
for all bounded Borel subsets . 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).