Let
points ,
...,
be randomly distributed on a domain , and let be some event that depends on the positions of the points. Let be a domain slightly smaller than but contained within it, and let be the part of not in . Let be the probability of event , be the measure of , and the measure of , then Crofton's formula states that

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309-317, 1989.Ruben, H. and Reed, W. J. "A More General Form
of the Theory of Crofton." J. Appl. Prob.10, 479-482, 1973.Solomon,
H. "Crofton's Theorem and Sylvester's Problem in Two and Three Dimensions."
Ch. 5 in Geometric
Probability. Philadelphia, PA: SIAM, pp. 97-125, 1978.