分布数列的相等和极限

In the new axiom system, CBH system, put by author, the random variable is defined as a kind of distribution sequence which can be divided to any n distribution sequences mutually independent. Here the distribution sequence is defined as that its limits of frequency to drop in any measurable set of real number are exists and the limits are called probabilities. This paper researches the distribution sequence further more. The results of research of cause can use to random variables. First the problems of equals of two distribution sequences are researched, and give the four concept of completely equal, equal with probability one, equal with probability and equal with r rank. Then the problems of limits of countable distribution sequences are researched. So the definition of limits of completely convergence, of convergence with probability one, of convergence with probability and of r rank convergence. These definitions is compatible with that given by traditional probability theory, but the concepts will be more clear.