郑州大学学报（理学版）
鄭州大學學報（理學版）
정주대학학보（이학판）
JOURNAL OF ZHENGZHOU UNIVERSITY(NATURAL SCIENCE EDITION)
2007年
4期
1-9
,共9页
随机现象%集合%状态安排%事件%试验%概率测度
隨機現象%集閤%狀態安排%事件%試驗%概率測度
수궤현상%집합%상태안배%사건%시험%개솔측도
random phenomena%set%state arrangement%event%trial%probability measure
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.
對概率論基礎歷來有多元的認識,歷史上不同觀點的爭論(如客觀與主觀)持續不斷.如今Kolmogorov 公理模型在數學中被廣汎接受.但是它隻是說:"概率"是一箇正則化測度,恰如長度、體積、質量一樣,併且與隨機現象無關.事實上,概率和任意正則化的物理測度都滿足這箇公理繫統.所以它不是概率概唸的精確定義.本文嘗試給齣另一箇模型,它可縮小Kolmogorov模型與直觀揹景之間的間隙,統一歷史上的各種定義,併給一些爭論問題以閤理的解釋.
대개솔론기출력래유다원적인식,역사상불동관점적쟁론(여객관여주관)지속불단.여금Kolmogorov 공리모형재수학중피엄범접수.단시타지시설:"개솔"시일개정칙화측도,흡여장도、체적、질량일양,병차여수궤현상무관.사실상,개솔화임의정칙화적물리측도도만족저개공리계통.소이타불시개솔개념적정학정의.본문상시급출령일개모형,타가축소Kolmogorov모형여직관배경지간적간극,통일역사상적각충정의,병급일사쟁론문제이합리적해석.
There are pluralistic understandings on the foundation of probability theory and the disputes between different viewpoints (such as objective and subjective) have gone on for a long time in history. Nowadays, the Kolmogorov axiom model is widely accepted in mathematics. However, this model only says that "probability" is a normalized measure, just like length, volume, mass, etc, and irrelevant to random phenomena. In fact, the probability as well as any normalized physical measure fulfills the same axiom system. So it is not a precise definition of probability. Another model is presented, which reduces the gap between the Kolmogorov model and the intuitive background, unifies different definitions in history, and gives reasonable explanations to some dispute issues.
