J Austral Math Soc Ser A 45 pp133--141, 1988.

Ergodic Measures for the Irrational Rotation on the Circle

William Moran

Abstract

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-Stietjes coefficients vanishing at infinity. We show further that these are the unique quasi-invariant measures on T with their associated Radon-Nikodym derivative.

1980 AMS Subject Classification: 28D99, 42A38

Browse the article

Authors

William Moran

Department of Pure Mathematics, The University of Adelaide, Adelaide, South Australia 5000, Australia.