A more general form of a theorem of Crofton
Harold Ruben, William J. Reed · Journal of Applied Probability · 1973
Let Dj be a domain in nj,-dimensional Euclidean space, for j = 1, …, k. Suppose that for each j = 1,…, k, Nj points are chosen independently at random in Dj. A theorem, which is an extension of a theorem of Crofton, is proved about the expected value of functions of the points.