# Probability – Show that the number of elements in a given set is a Poisson process.

To let $$quad { nu_n, xi_k ^ n } in mathbb N$$ to be a family of random variables. $$quad nu_n sim Poiss ( lambda), quad xi_k ^ n sim Unif (n-1, n],$$
To let $$quad N_t = | {(k, n): k le nu_n, quad xi_k ^ n le t } |.$$
I have to show that $$N_t$$ is Poisson process on $$[0+infty)[0+infty)[0+infty)[0+infty)$$ and I have trouble proving the definition (I use the definition of the Poisson process as the Levy process). For hints, I would be very thankful.