柯尔莫戈罗夫的公理化理论及其概率思想

A Research on A.N.Kolmogorov's Axiomization Theory and Other Probability Theory

概率论是现代数学的主流分支之一,其数学基础是柯尔莫格罗夫所建立的概率论公理体系。概率论公理体系不仅使概率理论的形式结构清晰、逻辑推理严密,而且还使概率论本身及形式结构与之相近的其他数学理论都取得了实质性的进展。柯尔莫格罗夫自20世纪20年代初开始研究概率论公理化系统。1929年在论文"一般测度论和概率论的计算"中论述了在测度论基础上的概率论公理化方法,1933年以德文出版了《概率论基础》,该书标志着概率论从半物理性质的科学转变成具有严密逻辑基础的数学分支。

The theory of probability axiomatics has not only caused the probability mathematics theory the form structure clearly and the logic reasoning to be strict,moreover also has caused theory of probability itself and the close other mathematics theory have all made the substantive progress. A.N.Kolmogorov was one of the famous mathematicians during the twentieth century. He was the founder of one of the probability subjects. From the 1920＇s he study the theory of probability axiomization system.In 1929 Kolmogorov published ＂General Measure Theory and Calculation of Probabilities＂ ,in this paper he had discussed in the foundation in the measure the theory of probability axiomization method. In 1933 he published ＂Theory of Probability Foundation＂ by the German,this book symbolized the theory of probability transformed from half physical property science has the strict logical foundation mathematics branch. Moreover he popularized the Law of Large Numbers theory and established axiomatic system of probability theory and laid a Markov process theory and study the stationary process and so on. He created a new chapter in probability theory.