A simultaneous version of Host’s equidistribution Theorem
A simultaneous version of Host’s equidistribution Theorem
Let $\mu$ be a probability measure on $\mathbb {R}/\mathbb {Z}$ that is ergodic under the $\times p$ map, with positive entropy. In 1995, Host showed that if $\gcd (m,p)=1$, then $\mu$ almost every point is normal in base $m$. In 2001, Lindenstrauss showed that the conclusion holds under the weaker …