对概率模型的认识

对概率论基础历来有多元的认识,历史上不同观点的争论(如客观与主观)持续不断.如今Kolmogorov公理模型在数学中被广泛接受.但是它只是说:"概率"是一个正则化测度,恰如长度、体积、质量一样,并且与随机现象无关.事实上,概率和任意正则化的物理测度都满足这个公理系统.所以它不是概率概念的精确定义.本文尝试给出另一个模型,它可缩小Kolmogorov模型与直观背景之间的间隙,统一历史上的各种定义,并给一些争论问题以合理的解释.

An Understanding of Probability Models

There are pluralistic understandings on the foundation of probability theory and the disputes between different viewpoints (such as objective and subjective) have gone onfor along ti mein history.Nowadays,the Kol mogorov axiom model is widely acceptedin mathematics.However,this model only says that"probability"is a normalized measure,just like length,volume,mass,etc,andirrelevant to randomphenomena.In fact,the probability aswell as any normalized physical measure fulfills the same axiomsystem.Soit is not a precise definition of probability.Another model is presented,which reduces the gap between the Kol mogorov model and the intuitive back-ground,unifies different definitions in history,and gives reasonable explanations to some dispute issues.