Let M denote a Poisson process on Rd + with intensity μ. Show that N(t) = M((0, t] d), for t ≥ 0, is a Poisson process on R+ with E[N(t)] = μ((0, t] d). This fact for d = 2 provides an alternate...

Let M denote a Poisson process on Rd + with intensity μ. Show that N(t) = M((0, t] d), for t ≥ 0, is a Poisson process on R+ with E[N(t)] = μ((0, t] d). This fact for d = 2 provides an alternate approach to proving the departure process in an Mt/Gt/∞ system is Poisson; see Section 3.12.