Some remarks on -adic Riesz products

We study the precise conditions for mutual absolute continuity and mutual singularity of two p -adic Riesz products, defined respectively by two coefficients sequences a k , b k . Our conditions are different from that appear in (Fan and Zhang, 2009) [6]. This paper can be viewed as a generalization of (Fan and Zhang, 2009) [6] in this topic. We also calculate the Hausdorff dimension of Riesz products.