# Rudolph's theorem on the Furstenberg conjecture

### Joachim Cuntz (University of Muenster)

Tuesday 5th March, 2013 16:00-17:00 Maths 203

#### Abstract

Rudolph's theorem states: Let p and q be two natural numbers which are relatively prime. Assume that $\mu$ is a measure on the unit interval which is invariant and ergodic for the two transformations given by multiplication by p and q mod 1. If $\mu$ is not Lebesgue
measure, then both transformations have entropy 0 with respect to $\mu$. We try to sketch a proof of this theorem.