Invariant measure for double base expansions

Wenduo Huang, Vilmos Komorni, Yuru Zou

Given a pair $Q=(q_0,q_1)\in (1,\infty {)}^2$ with $q_0+q_1\ge q_0{q}_1$, a sequence $(c_i)\in \{0,1{\}}^{\infty }$ is called a $Q$-expansion of $x$ if<br/>\begin{equation*}<br/>x=\sum_{i=1}…