Let's consider $X = \{1, 2, \ldots, n \}$. I would like to establish, how many of the maps $f: X \to X$ have the following strong mixing property:
For a given triple $(X, \mathcal{B}, \mu)$, $T: X \to X$ is strong mixing, if it preserves measure and the shares the following property $\mu(T^{-n}(A) \cap B) \rightarrow \mu(A) \mu(B)$, as $n \to \infty$
Then, after several attempts i've found it quite challenging to find a general approach to the problem that might work. (after considering some cases in particular)
Are there any hints that might help?