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Geometrical properties and other background material
Stationary Voronoi tessellations
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Analysis angle arbitrary assume ball Borel set boundary bounded Borel set Brakke centroid constitute a tessellation contains d-n+k d-polytope defined Delaunay cells Delaunay edge Delaunay tessellation denotes density e.g. Stoyan equivariant Exercise facets Figure formula Fubini's theorem Gabriel neighbours Hadwiger's theorem homogeneous Poisson process implies integral geometry intensity intersection invariant under translations isotropic k-dimensional k-facets k-flat Lebesgue measure Lecture Notes Lemma line segment locally finite manuscripts Mathematical measurable function Moller non-negative measurable function nuclei nullset number of vertices obtain order moments Palm distribution Palm measure planar section point process Poisson point process Poisson-Voronoi cell Proposition 3.2.3 Quine and Watson random Voronoi tessellations Remark Section 3.1 simulated spatial point process spatial Voronoi Springer-Verlag stochastic geometry tessella tion topological interiors translation invariant typical Poisson-Delaunay cell typical Poisson-Voronoi typical Voronoi cell Verify vertex void-probabilities volume Voronoi and Delaunay Voronoi cell C(x Voronoi edges Voronoi tessellation