I have the exercise to show that a rigid rotation on a torus is ergodic given that $\langle \omega , j \rangle \notin \mathbb{Z}$ for all $j \in \mathbb{Z}^n$.
I tried showing that the for all integrable functions $f$ the fact $f(\varphi(x))=f(x)$ implies that $f$ is constant almost everywhere. But that's all I have so far.
Thanks for your help.
Here you can find the exercise:
