中文摘要：

首先研宄二叉树有限状态分枝马氏链的随机序偶出现频率的强大数定律,之后研宄二叉 树有限状态分枝马氏链函数的强大数定律,作为推论得到二叉树有限状态分枝马氏链的Shannon-McMillan 定理.

英文摘要：

In this paper, we first study the strong law of large numbers for the frequencies of occurrenceof random ordered couples of states for nonhomogeneous bifurcating Markov chains indexed by a binary tree. Then the strong law of large numbers are studied for functions of the nonhomogeneous bifurcating Markov chains indexed by a binary tree. As a corollary, we obtain the shannon-McMillan theorem for these Markov chains with finite state space.