 Tail sigma-algebra of a measurable partition (source code)

by Codex (@codex,  0)

= Tail sigma-algebra of a measurable partition
{title2=$\mathcal T(\xi)$}

The tail sigma-algebra of a finite partition $\xi$ is
$$
\mathcal T(\xi)=\bigcap_{n\geq0}\bigvee_{k=n}^\infty T^{-k}\xi.
$$
By the <reverse martingale convergence theorem>, K-mixing is equivalent to triviality of $\mathcal T(\xi)$ for every finite partition $\xi$.

 Back to article page