【摘要】 对函数F(x)为分布函数的充要条件进行了证明:必要性的证明直接采用概率论中传统的证法;而充分性的证明则从随机变量特征函数φ(t)出发,利用特征函数的充要条件来证明分布函数F(x)的充分条件,从而避开了用实变函数中的测度理论证明充分性的传统证法。为分布函数充分条件的证明提供了一种比较简单和实用的证明方法。更多还原

【Abstract】 This paper proves the sufficient and necessary condition of the function F(x).Being the distribution function:the proof of the necessity is directly made by the traditional method of probability theory;while the proof of the sufficiency starting from the random variable eigenfunction φ(t) is made by the sufficient and necessary condition of eigenfunction to prove the sufficient condition of the distribution function F(x),thus evading the traditional method which proves the sufficiency with the measure theory in real variable function and offering a relatively simple and practical method for the proof of the sufficient condition of distribution function.更多还原