  It is shown that a certain class of Riesz product type measures on
$\mathbb{R}$ is realized a spectral type of rank one flows. As a consequence,
we will establish that some class of rank one flows has a singular spectrum.
Some of the results presented here are even new for the $\mathbb{Z}$-action.
Our method is based, on one hand, on the extension of
Bourgain-Klemes-Reinhold-Peyri\`ere method, and on the other hand, on the
extension of the Central Limit Theorem approach to the real line which gives a
new extension of Salem-Zygmund Central Limit Theorem. We extended also a
formula for Radon-Nikodym derivative between two generalized Riesz products
obtained by el Abdalaoui-Nadkarni and a formula of Mahler measure of the
spectral type of rank one flow but in the weak form. We further present an
affirmative answer to the flow version of the Banach problem, and we discuss
some issues related to flat trigonometric polynomials on the real line in
connection with the famous Banach-Rhoklin problem in the spectral theory of
dynamical systems.
