Is the $T$-function $f(x) = (x \text{AND} c) + (x^2 \text{OR} c)$, where $c$ is positive integer ergodic in the space $Z_2$ (p-adic numbers)?
What is the measure of this function?
I am trying to use this theorem
My progress:
- x = x^2 in $Z_2$
Found out that f1(x) = (x AND c), f2(x) = (x OR c) are uniformly differentiable in $Z_2$
- It remains to prove transitivity of f(x) ( Based on this theorem)
transitivity means that the function is a full-cycle permutation.
- I am trying to prove transitivity based on this example
