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Flat sections of random tessellations
Voronoi and Delaunay tessellations generated by a stationary Poisson point process
1 other sections not shown
angle sum arbitrary Borel sets cells which contain centroids Corollary 5.4 countable set covariant d-dimensional d-polytope d+1)-simplex defined w.r.t. denotes expectation ergodic theory Euclidean space exterior angle facet characteristics Formula Furthermore Hence hyperplanes integral geometry intersection invariant under motions invariant under translations isotropic JtEt Ld-s Lebesgue measure Lemma marked point process mean value relations measurable function Mecke Miles non-negative and measurable normal tessellation normal with probability number of t-facets observed inside Palm distribution Palm measure theory Poisson point process polytope probability measure Proposition 3.1 Quermassintegral random tessellation relative boundaries relative interior right hand side s-content s-facets contained s-flat s-subspace sectional Voronoi tessellation side of 6.5 stationary Poisson point stereological Stoyan subsets t-flat F tessella tessellation characteristics tessellation is given Theorem 6.3 typical cell typical s-facet unit ball vertex vertices Voronoi and Delaunay w.r.t. the typical XeSs(m,Y YeSs(m,X