Suppose that f R* = [a, c] for all c (a, b) and that there exists (a, b) and

Suppose that f ∈ R* = [a, c] for all c ∈ (a, b) and that there exists γ ∈ (a, b) and ω ∈ L[a, b] such that |f(x)| < v(x) for x ∈ [γ, b]. Show that f ∈ R* = [a, b].