Let $T$ be a process defined on compact of 2 - adic numbers. $T(x)=x+1$. 2-adic numbers can be represented as binary number $x=\sum_{k=0}^{\infty} x_k * 2^k$. In this case, the transformation $T$ is given by $T(1,…,1,0,X_{k+1},X_{k+2},…)=(0,…,0,1,,X_{k+1},X_{k+2},…)$. I need to proof that $T$ is ergodic. How strictly it can be proved?
Thank you in advance.