A random closed set (RACS) in 
is a measurable function
from a probability space 
into 
where 
is the collection of all closed subsets of 
and where 
denotes the sigma-algebra
generated over 
the by sets
 |
for all compact subsets 
.
Originally, RACS were defined not on 
but in the more general setting of locally
compact and separable (LCS) topological
spaces (Baudin 1984) which may or may not be T2.
In this case, the above definition is modified so that 
is defined to be the collection of closed subsets of some
ambient LCS space 
(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).
