Some remarks on \(p\)-adic Riesz products (Q394911)

The authors study Riesz products of the form \(\mu_a= \prod(1+ \text{Re\,}a_k,\gamma_k)\) where \(\gamma_k\) are characters on the ring of \(p\)-adic integers. They characterize the mutual absolute continuity versus mutual singularity of \(\mu_a\) and \(\mu_b\) provided the sequences \((|a_k|)\) and \((|b_k|)\) do not both tend to 1 too quickly. They also calculate the Hausdoff dimension of \(\mu_a\). Their methods are largely probabilistic.