On the dimension of Bernoulli convolutions for all transcendental parameters

The Bernoulli convolution ${\nu }_{\lambda }$ with parameter $\lambda \in (0,1)$ is the probability measure supported on $\mathbf{R}$ that is the law of the random variable $\sum \pm {\lambda }^n$, where the $\pm$ are independent fair coin-tosses. We prove that $\dim {\nu }_{\lambda }=1$ for all transcendental $\lambda \in (1\mathrm{/}2,1)$.