K-mixing

A system is K-mixing when every finite partition becomes asymptotically independent of every event in its remote future: if ${\mathcal{F}}_n(\xi )={\bigvee }_{k=n}^{\infty }{T}^{-k}\xi$, thenfor every measurable $A$ and every finite $\xi$.

The tail sigma-algebra of a finite partition $\xi$ isBy the reverse martingale convergence theorem, K-mixing is equivalent to triviality of $\mathcal{T}(\xi )$ for every finite partition $\xi$.