=+a stochastic process [X 4: A € T ] such that (i) X , has the Poisson distribution with mean v( A) and (ii) X4 ....., X, are independent if A1 ,..., A ,, are disjoint. Hint: To define the finite-dimensional distributions, generalize this construction: For A, B in T, consider independent random variables Y1, Y2, Y;

having Poisson distributions with means v(An BC), v( An B), v(AB); take HA, B to be the distribution of (Y) + Y2, Y2 + Y,).