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Alternative forms of the integral geometric density of an r -subspace r -flat containing q q + 1 points in euclidean n -space R n are given Stochastic applications in R 3 include formulae for (i) the mean area of intersection of a domain by an isotropic plane through the origin; and (ii) the variance of the area of intersection of a domain by an isotropic uniform plane.
R. E. Miles (Sat,) studied this question.
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