  The notion of Riesz sets tells us that a support of Fourier transform of a
measure with non-trivial singular part has to be large. The notion of Rajchman
sets tells us that if the Fourier transform tends to zero at infinity outside a
small set, then it tends to zero even on the small set. Here we present a new
angle of an old question: Whether every Rajchman set should be Riesz.
