Riesz products on the ring of dyadic integers
In this paper a class of Riesz products on the ring of dyadic integers is introduced. Using almost everywhere convergence of certain series, Hausdorff dimension of these Riesz products is determined. Other properties, such as mutually absolute continuity, quasi-invariance and quasi-Bernoulli property, are also discussed. In the previous paper [C. R., Math., Acad. Sci. Paris 344, No. 7, 425--430 (2007; Zbl 1169.28001)] \textit{A. Fan} and the author introduced a class of probability measures, called Riesz products, on the ring \(\mathbb Z_p\) of \(p\)-adic integers. They proved a result on the almost everywhere convergence, with respect to a Riesz product, of some related series and then obtained the Hausdorff dimension of the Riesz product.
scientific article; zbMATH DE number 5568974