A proof of Furstenberg's conjecture on the intersections of $\times p$ and $\times q$-invariant sets

Meng Wu

We prove the following conjecture of Furstenberg (1969): if $A,B\subset [0,1]$ are closed and invariant under $\times p\mathrm{mod}1$ and $\times q\mathrm{mod}1$, respectively, and if $\log p/…