In this paper we provide definitions for the local mean volume and mean surface densities of an inhomogeneous random closed set. "A relation between the local spherical contact distribution function and the local surface density is proven. This relation is valid under a regularity condition on the random set involved, whose field of applicability is analysed in detail. Explicit expressions for the local volume and surface densities of a type of inhomogeneous Boolean models are also provided.
The local mean volume and surface densities for inhomogeneous random sets / V. Capasso, A. Micheletti. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. SUPPLEMENTO. - ISSN 1592-9531. - 65:1(2000), pp. 49-66. (Intervento presentato al 3. convegno Stochastic Geometry , Convex Bodies and Empirical Measures tenutosi a Mazara del Vallo nel 1999).
The local mean volume and surface densities for inhomogeneous random sets
V. CapassoPrimo
;A. MichelettiUltimo
2000
Abstract
In this paper we provide definitions for the local mean volume and mean surface densities of an inhomogeneous random closed set. "A relation between the local spherical contact distribution function and the local surface density is proven. This relation is valid under a regularity condition on the random set involved, whose field of applicability is analysed in detail. Explicit expressions for the local volume and surface densities of a type of inhomogeneous Boolean models are also provided.
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