The equality cases $P_t(\mathbb{N})=\frac{1}{2}$ for the deconvolved sum-of-digits measures

Dawid Tarłowski

Let $s(n)$ denote the number of ones in the binary expansion of an integer $n\in \mathbb{N}$, and let ${\mu }_t$ be the probability measure on $\mathbb{Z}$ defined by the asymptotic dens…