On the Lévy–Raikov–Marcinkiewicz theorem

Let μ be a finite non-negative Borel measure. The classical Lévy–Raikov–Marcinkiewicz theorem states that if its Fourier transform μˆ can be analytically continued to some complex halfneighborhood of the origin containing an interval (0, iR) then μˆ admits analytic continuation into the strip {t: 0 < t