  We construct certain Rajchman measures by using integrability properties of
the Fourier and Fourier-Stieltjes transforms. In particular, we state a problem
and prove that it is equivalent to the known and still unsolved question posed
by R. Salem (Trans. Amer. Math. Soc. 53 (3) (1943), p. 439) whether
Fourier-Stieltjes coefficients of the Minkowski's question mark function vanish
at infinity.
