>>578の続き

(1) と (2) より

g(t, μ + h) - g(t, μ) - ψ(t, μ)h
= ∫[t_0, t] (f(s, g(s, μ + h), μ + h) - f(s, g(s, μ), μ)) ds
- ∫[t_0, t] (d_2)f(s, g(s, μ), μ)ψ(s, μ)h ds
- ∫[t_0, t] (d_3)f(s, g(s, μ), μ)h ds ← (3)

ここで
α(s, h) = f(s, g(s, μ + h), μ + h) - f(s, g(s, μ), μ + h)
- (d_2)f(s, g(s, μ), μ + h)(g(s, μ + h) - g(s, μ))

β(s, h) = f(s, g(s, μ), μ + h) - f(s, g(s, μ), μ)
- (d_3)f(s, g(s, μ), μ)h

γ(s, h) = (d_2)f(s, g(s, μ), μ + h)(g(s, μ + h) - g(s, μ) - ψ(s, μ)h)

λ(s, h) = ((d_2)f(s, g(s, μ), μ + h) - (d_2)f(s, g(s, μ), μ))ψ(s, μ)h
とおく。

(3) より
g(t, μ + h) - g(t, μ) - ψ(t, μ)h
= ∫[t_0, t] α(s, h) ds
+ ∫[t_0, t] β(s, h) ds
+ ∫[t_0, t] γ(s, h) ds
+ ∫[t_0, t] λ(s, h) ds ← (4)

(続く)