Random Tessellations in RdDepartment of Theoretical Statistics, Institute of Mathematics, University of Aarhus, 1986 - Geometric probabilities - 79 pages |
Contents
Flat sections of random tessellations | 5-20 |
Voronoi and Delaunay tessellations generated by | 7 |
References | |
Common terms and phrases
AARHUS angle sum arbitrary Borel sets centroids Corollary 5.4 countable set covariant d-dimensional d-polytope d-s+u defined w.r.t. denotes expectation ergodic theory Euclidean space exterior angle facet characteristics follows Formula Furthermore Hadwiger Hence hyperplanes integral geometry intersection invariant under motions isotropic JtEt La-s Lebesgue measure Lemma mean value relations measurable function Mecke Miles motions in Rd non-negative and measurable normal tessellation number of t-facets observed inside Ost≤d Palm distribution Palm measure theory Poisson point process Poisson process polytope probability measure Proposition 3.1 Quermassintegral random tessellation relative boundaries right hand side s-content s-facets contained s-flat s-r+q s-subspace S(Ru side of 6.5 stationary Poisson point stereological stereology Stochastic Geometry subsets tessella tessellation characteristics tessellation in Rd tessellation is given Theorem 6.3 typical cell typical s-facet vertices Voronoi and Delaunay Voronoi tessellation YES m,x YES(m,x Ε Σ ΕΦ Σ Σ