Expectation formulas and isoperimetric properties for non‐isotropic Boolean models

Boolean models Y in R2 and R3 are considered and formulas connecting the quermass densities of Y with the mean values of certain functional of the primary grain are given in the non‐isotropic case. Under symmetry conditions, the mean functionals are interpreted as mixed volumes of convex bodies which are associated with Y. Extremal properties of isotropic Boolean models are deduced from the isoperimetric inequality.

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