Purity results for some arithmetically defined measures
Peter J. Grabner · arXiv (Cornell University) · 2019
We study measures that are obtained as push-forwards of measures of maximal entropy on sofic shifts under digital maps $(x_k)_{k\in\mathbb{N}}\mapsto\sum_{k\in\mathbb{N}}x_kβ^{-k}$, where $β>1$ is a Pisot number. We characterise the continuity of such measures in terms of the underlying automaton and show a purity result.