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Proof.
The first two items are easy consequences of the previous Lemma. For the last item we simply notice that for C ≥ 1 C\geq 1
(4.139) ∫ − C − 1 h ( u ) 𝑑 u = ∫ − C − 1 ( T 2 − n ( T + k − u ) n − 1 + ϵ ( u ) ) 𝑑 u ≤ C T . \int_{-C}^{-1}h(u)du=\int_{-C}^{-1}(T^{2-n}(T+k_{-}u)^{n-1}+\epsilon(u))du\leq CT.