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Zbl 0687.43001
Parreau, François
Ergodicité et pureté des produits de Riesz. (Ergodicity and purity of Riesz products). (French)
[J] Ann. Inst. Fourier 40, No.2, 391-405 (1990). ISSN 0373-0956; ISSN 1777-5310/e

It is shown that Riesz products on the torus are ergodic measures under a lacunarity condition for their frequencies, without any arithmetic requirement, and that the given condition is the best possible from this viewpoint. A similar criterion is given for the purity property previously discussed by {\it B. Host} and the author [C. R. Acad. Sci., Paris, Sér. I 306, 409-412 (1988; Zbl 0653.22006)] and this provides an example of a pure measure which is singular to all its translates and henceforth not ergodic.
[F.Parreau]

MSC 2000:: *43A05 Measures on groups, etc.
42A55 Lacunary series
22D40 Ergodic theory on groups
28C10 Set functions and measures on topological groups

Keywords: Riesz products; ergodic measures; lacunarity condition; purity; pure measure

Citations: Zbl 0653.22006

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