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===Random set of points===
A point process 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"> A. Baddeley, I. Barany, and R. Schneider. Spatial point processes and their applications. ''Stochastic Geometry: Lectures given at the CIME Summer School held in Martina Franca, Italy, September 13–18, 2004'', pages 1–75, 2007.</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"> R. Schneider and W. Weil. ''Stochastic and integral geometry''. Springer, 2008.</ref>
A point process is often denoted by a single letter <ref name="kingman1992poisson">[[J. F. C. Kingman]]. ''Poisson processes'', volume 3. Oxford university press, 1992.</ref><ref name="moller2003statistical"> J. Moller and R. P. Waagepetersen. ''Statistical inference and simulation for spatial point processes''. CRC Press, 2003.</ref><ref name="stoyan1995stochastic"/>, for example <math> \Phi</math>, and if the point process is considered as a random set, then the corresponding notation<ref name="stoyan1995stochastic"/>:
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