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a-algebra a-field angle arbitrary avoidance function Baire set Borel sets c-traps canonical model circle condition consider continuous converges convex convex polygons corresponding countable covariance measure cylinder D. G. Kendall defined definition denote density disjoint distance distribution domain doubly stochastic Poisson equivalent ergodic Euclidean example exists finite fixed follows formula Fubini's theorem given hence homogeneous implies independent inequality infinite integral geometry intersection interval invariant Kakutani Lebesgue measure Lemma length line-processes M. S. Bartlett Math mixed Poisson process name-class number of points obtain orthogonal plane planned path polygons polytope probability measure Proof properties prove random closed set random measure random sets random tessellation random variable real line result right-hand side sampling satisfies second-order stationary Section sequence space standard modification Statistical stochastic process strictly stationary strong incidence function subset subshapes Suppose Theorem topology traps unique unlabelled shapes weak incidence function zero