On Some Qualitative Properties of the Boolean Model of Stochastic Geometry
Dietrich Stoyan · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1979
Abstract For the Boolean model, one of the basic models of stochastic geometry and stereology, monotonicity and continuity properties are proved. In particular, for Boolean models on the line the relation between primary and number granulometry is discussed, and monotonicity properties of the covariance function are studied. Finally, the probability of hitting of an arbitrary primary grain by one of the other ones is considered.