We prove an analogue of the classical zero-one law for both homogeneous and nonhomogeneous Markov chains (MC). Its almost precise formulation is simple: given any event A from the tail σ-algebra of MC $(Z_n)$, for large n, with probability near one, the trajectories of the MC are in states i, where $P(A|Z_n=i)$ is either near 0 or near 1. A similar statement holds for the entrance σ-algebra when n tends to $-\mathrm{\infty }$. To formulate this second result, we give detailed results on the existence of nonhomogeneous Markov chains indexed by ${\mathbb{Z}}_{-}$ or $\mathbb{Z}$ in both the finite and countable cases. This extends a well-known result due to Kolmogorov. Further, in our discussion, we note an interesting dichotomy between two commonly used definitions of MCs.

我们证明了均匀和非均匀马尔可夫链（MC）的经典零一定律的类似物。它几乎精确的公式很简单：给定来自MC的尾σ代数的任何事件A$(Z_n)$，对于较大的n，概率接近 1，MC 的轨迹处于状态i，其中$磷(\mathrm{一个}|Z_n=\mathrm{一世})$接近 0 或接近1。当n趋于$-\mathrm{\infty }$. 为了制定第二个结果，我们给出了关于非齐次马尔可夫链存在的详细结果，索引为${\mathbb{Z}}_{-}$或者$\mathbb{Z}$在有限和可数的情况下。由于 Kolmogorov，这扩展了一个众所周知的结果。此外，在我们的讨论中，我们注意到两个常用的 MC 定义之间存在有趣的二分法。