6.19 Let X be an r.v. with characteristic function . Then for every x R we have P(X = x) = limT 1 2T

6.19 Let X be an r.v. with characteristic function ϕ. Then for every x ∈ R we have P(X = x) = limT→∞

1 2T

 T

−T e−itxϕ(t)dt.

Deduce that if ϕ(t) → 0 as |t|→∞ then P(X = x)=0 for all x ∈ R.