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).