N(t) converges to infinity almost surely
As t tends to infinity, m(t) tends to infinity
By assumption, the first moment of the interarrival time, E(U), is strictly positive and finite
Obtaining E(T_{N(t)+1}) using Wald's identity (T_n is the time of the nth arrival--the sum of the first n interarrival times)
First part of proof: liminf t→ ∞ m(t)/t ≥ 1/E(U)
Second part of proof: limsup t→ ∞ m(t)/t ≤ 1/E(U)

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