Point process notation: Difference between revisions

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==Dual notation==
 
The different interpretations of point processes as random sets and counting measures is captured with the often used notation <ref name="stoyan1995stochastic"/><ref name="moller2003statistical"/><ref name="BB1"> F. Baccelli and B. B{\l}aszczyszyn. ''Stochastic Geometry and Wireless Networks, Volume I --- Theory'', volume 3, No 3--4 of ''Foundations and Trends in Networking''. NoW Publishers, 2009.</ref> in which:
 
* <math> \Phi</math> isdenotes a set of random points.
 
* <math> \Phi(B)</math> isdenotes a random variable that gives the number of points of <math> \Phi</math> in <math> B</math> (hence it is a random counting measure).
 
Denoting the counting measure again with <math> \#</math>, this new dual notation would imply: