Published online by Cambridge University Press: 09 April 2009
Riesz products are employed to give a construction of quasi-invariant ergodic measures under the irrational rotation of T. By suitable choice of the parameters such measures may be required to have Fourier-Stieltjes coefficients vanishing at infinity. We show further that these are the unique quasi-invariant measures on T with their associated Radon-Nikodym derivative.