里斯表示定理前史的探析

The research of pre-history about the Riesz representation theorem

里斯(Frigyes Riesz 1880—1956)表示定理是几代数学家努力的结果,是分析与综合相结合的产物。文中基于对原始文献及历史背景及人物关系的研究,对里斯表示定理的前史进行了探析,主要对里斯表示定理的起源及形成进行梳理;在定理的形成过程中,阿达玛(Hadamard Jacques1865—1963),弗雷歇(Maurice Fréchet 1878—1973)及里斯分别以3种不同的积分工具,柯西(Louis Cauchy 1789—1857)积分,勒贝格(Henri leon Lebesgue 1875—1941)积分和斯蒂尔杰斯(Thomas Joannes Stieltjes 1856—1894)积分,推进了里斯表示定理的发展。

Riesz representation theorem is the outcome of the efforts of several generations of mathematicians, is the products of analysis combined with the composition. Based on the original documents and historical background study and studying on the relationship between the characters, the former history of Riesz representation theorem is analyzed in the article, mainly to clarify the origin and formation of Riesz representation theorem. In the forming process of the theorem, Adama, Freehet and Riesz respectively extended the Riesz representation theorem by three different integration tools, namely cauchy integral, Lebesgue integral and Stiehjes integral.