A point process ''Φ'' is called ''simple'' if no two (or more points) coincide in ___location with [[Almost surely|probability one]]. Given that often point processes are simple and the order of the points does not matter, a collection of random points can be considered as a random set of points<ref name="stoyan1995stochastic"/><ref name="baddeley2007spatial">{{cite doi|10.1007/978-3-540-38175-4_1}}</ref> The theory of random sets was independently developed by [[David George Kendall|David Kendall]] and [[Georges Matheron]]. In terms of being considered as a random set, a sequence of random points is a random closed set if the sequence has no [[Limit point#Types of limit points|accumulation points]] with probability one<ref name="schneider2008stochastic">{{cite doi|10.1007/978-3-540-78859-1}}</ref>
A point process is often denoted by a single letter,<ref name="stoyan1995stochastic"/><ref name="kingman1992poisson">[[J. F. C. Kingman]]. ''Poisson processes'', volume 3. Oxford university press, 1992.</ref><ref name="moller2003statistical">{{cite doi|10.1201/9780203496930}}</ref> for example <math> \Phi</math>, and if the point process is considered as a random set, then the corresponding notation:<ref name="stoyan1995stochastic"/>
