1.8 Prove Corollary 1.14. [Hint: Show that (a) (v) = E0(X v) M as v...

1.8 Prove Corollary 1.14. [Hint: Show that

(a) φ(v) = E0ρ(X − v) → M as v → ±∞

and

(b) that φ is continuous;

(b) follows from the fact (see TSH2, Appendix Section 2)

that if fn, n = 1, 2,... and f are probability densities such that fn(x) → f (x) a.e., then

ψfn → ψf for any bounded ψ.]