definition of ergodic component: consider stationary dynamical system $(X, \mathcal{B}, \mu, T)$, each ergodic component is $m(\cdot)=\mathbb{E}_{\mu}^{\mathcal{I}}\mathbf{1}_{(\cdot)}$, $\mathcal{I} $ is invariant $\sigma$-algebra. To explain it, $X$ can be divided into disjoin sets, supp of $m$ is one of this set, $T$ is closed on this set, $m$ is ergodic on this set. so it looks like sub ergodic system on a smaller set.

however, I could not find the definition of mixing component. is the definition similar? can you refer some materials about it? Thanks!