Information theoretic study of empirical probability

我们探讨了经验概率的信息论研究。主要结果如下：1）基于有限型拟对称散度函数，得到了两种不同可计算概率测度的新的Martin-Loef随机性准则。2)基于Lynch-Davisson通用编码算法给出了对策论大数定律的另一种证明，并指出了将大数定律和意见收敛定理推广到一般预测对策的可能性.

We explored an information theoretic study of empirical probability. The main results are summarized as follows: 1) A novel Martin-Loef randomness criterion for two distinct computable probability measures was obtained based on finite-type quasi-symmetric divergence functions. 2) An alternative proof of a game-theoretic law of large numbers was given based on the Lynch-Davisson universal coding algorithm, and a possibility of generalizing the law of large numbers and the theorem of convergence of opinions to a general prediction game was pointed out.