stylistic:style_transfer
Factorial moment measure

For a general Poisson point process with intensity measure Λ {\displaystyle \textstyle \Lambda } the n {\displaystyle \textstyle n} -th factorial moment measure is given by the expression:

where Λ {\displaystyle \textstyle \Lambda } is the intensity measure or first moment measure of N {\displaystyle \textstyle {N}}, which for some Borel set B {\displaystyle \textstyle B} is given by

For a homogeneous Poisson point process the n {\displaystyle \textstyle n} -th factorial moment measure is simply:

where | B i | {\displaystyle \textstyle |B_{i}|} is the length, area, or volume (or more generally, the Lebesgue measure) of B i {\displaystyle \textstyle B_{i}}. Furthermore, the n {\displaystyle \textstyle n} -th factorial moment density is: