A random closed set (RACS) in 
is a measurable function from a probability
space 
into 
where 
is the set of all closed subsets of 
and where 
denotes the sigma-algebra
generated over 
by the sets
 |
.
The classical setting is a locally compact, separable T2-space 
(Matheron 1975, Molchanov 2005). The
definition then uses all closed sets in 
and all compact sets 
. More general settings, including spaces without
the Hausdorff assumption, are also considered (Molchanov
2005).
Despite a number of apparent differences, one can show that multidimensional point processes are a special case of RACS when talking about 
(Baudin 1984).
