Since ∀η ∃δ such that |h|＜0 ⇒ |f(a+h)-f(a)|＜η,
|ε|＜δ ⇒ ∀θ |f(a+εe^iθ)-f(a)|＜η, therefore |∫f(a+εe^iθ)-f(a)dθ|＜πη,
i.e. lim_[ε→0] ∫f(a+εe^iθ)-f(a)dθ= 0.