A Historical Research On Axiomatic Process Of Probability Theory

Since probability theory was born,it has developed into one of the mainstream branch of modern mathematics from the initial analysis of gambling problem.The direction and methods of modern probability theory have received a great development,especially for the last ten years,probability theory and other disciplines had gradually crossed, some new branch and growth point that have achieved outstanding results in scientific research and practical application has been formed.All these achievements are due to the establishment of the axiomatic system of probability theory.Kolmogorov’s axiomatic system in1933has so far become the most widely accepted foundation of probability theory. The establishment of axiomatic system indicated probability theory became a branch of mathematics that has a solid logical foundation.Therefore,the study on the history of probability theory,especially its history of axioms,is important for us to investigate the change of probabilistic thinking and its future development.In19th century, probability theory had accumulated many important achievements after the study of French mathematician Laplace and Poission and German mathematician Gauss and Russian mathematician chebyshev and else.Unfortunately,probability theory still lacked clear definition(such as probability,random events,random variables).Because there was no strict logical foundation so that some paradox emerged.The most famous of which was a paradox of geometric probability given by Bertrand who was a French mathematician.Paradox had sounded the alarm, mathematicians had to re-examine the mathematical foundations of probability theory.In1900,German mathematician Hilbert made a speech entitled "mathematical problem"on the Second International Congress of Mathematicians in Paris. He proposed twenty-three important problems that guided development of mathematics in20th century,the sixth problem related with axiomatization of probability theory.In1909,French mathematician Borel combined probability theory and measure theory for the first time and he defined the probability of countable sets of events. Relative to classical probability, this work expanded the understanding of probability.In1917,Soviet mathematician Bernstein builded the first axiom system of probability theory.In1919,Austrian mathematician Mises completed axiomation of the frequency definition and the statistical definition of probability.Some axiomatic system of subjective probability had also appeared.However,all these which were lack of rationality or lack of authority were just a prelude.Along with in-depth study of the law of large numbers and limit theory,mathematicians gradually became aware of that there were deep connections between probability theory and measure theory.Axiomatization of probability theory was really coming.In1933,Soviet mathematician Kolmogorov summarized the previous work and builded the system of probability theory which first based on measure theory in his book "The Grundbegriffe".The axiomatic system was accepted by most mathematicians,and then probability theory became one of the most important branch of modern mathematics and developed rapidly.In this article, I have analyzed a number of related material home and abroad on the history of probability theory.On the basis of previous work,the article combines with the study of the original literature and relies on representatives and their writings.It makes a general introduce to history of probability theory and focused on process of axiomatization.The most important is to investigate the outstanding achievements made by kolmogerov on axiomatic system of probability and tease out the overall evolution of axiomatic thinking of probability theory.