Dimension of Bernoulli Convolutions in ${\mathbb{R}}^d$

Ariel Rapaport, Haojie Ren

For $({\lambda }_1,...,{\lambda }_d)=\lambda \in (0,1{)}^d$ with ${\lambda }_1>...>{\lambda }_d$, denote by ${\mu }_{\lambda }$ the Bernoulli convolution associated to $\lambda$. That is, ${\mu }_{\lambda }$ is the distribution of the random vector $…