Abstract
The Boolean model is the basic random set model for many applications. Its main advantage lies in the fact that it is determined by a single measure-valued parameter, the intensity measure. Whereas classically Boolean models were studied which are stationary and isotropic, some of the methods and results have been extended to the non-isotropic situation. More recent investigations consider inhomogeneous Boolean models, i.e. random sets without any invariance property. Density formulae for inhomogeneous Boolean models make use of local variants of the classical quermassintegrals, the surface area measures and curvature measures. Iterations of translative integral formulae for curvature measures lead to further measures of mixed type.
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