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meet each other,they are not disturbed in their growth, which stop indepen- dently for each component. Let us transpose this description in terms of random sets. The points of the Poisson realization are in x. (i Ç I). The elementary grain is a nonstationary random set A'. Successively, we pick out various rea- i i lizations of A' from its space fi of définition and implant each A^ at the corresponding point x^. The différent A^ are thus indepent of each other. We will call the realization A of a Boolean scheme the union of the A. associated with a given realization of the points x^. A1 = UA! i e i The Boolean scheme is extremely fertile. It represents one of the first steps, in modelling, when one admits negligible interactions between the particles A.. We had the opportunity to use it in sedimentary petrography, in dendritic crystalline growth, in studies of forests, and ail its fields of application are probably not yet discovered. The basic study of the Boolean scheme has been made by Matheron. We center the primary grain AT at the origin. This random set is known by the datum of the two families of functionals Ô5(B) and x(B)* . w(B) = p(bca'| and x(B) = P (b f| A' ^ 0} (2) If A' is translated from the origin to the point z, it admits the new functionals ^Z(B) and easily deducible from (2) w (b) = p |bc a'| = p |b c a' } = 73(b ) (3) z z v -z ' -z xZ(B) = x(B_z) Let us consider now the Boolean scheme itself, namely the union of ail the A^, and compute the probability of B being included in the pores ^A of the scheme. According to the property (a) of the Poisson process, each element of volume dz of the space makes its contribution independently of the others. In dz, centered in z, two incompatible favourable events may happen : 1 - no germ in dz : probability l-0dz. t 2 - one germ in dz, but the grain A does not reach B : probability Gdz. x (B )• -z By composition of these two probabilities and summation in z extended to the space Rn, we find -e/n [1- x(B_z) ] dz Q(B) = P {B c[a | = e R (4) To interpret the geometrical meaning of the intégral in (4), let k(z) be the indicator function of the random set A'© B, that is k(z) = 1 when A' Q B^ ^ 0 k(z) = 0 when A? P) B^ = 0