中文摘要：

矩量问题是里斯解决第二类积分方程的主要途径。里斯通过对勒贝格平方可积函数集、连续函数集、勒贝格p幂可积函数集中的矩量问题的研究,发现了后两个函数集与勒贝格平方可积函数集的深刻差异。这一结果为巴拿赫空间理论及对偶空间理论的产生奠定了基础。

英文摘要：

Moment problem the moment problem in set Lebesgue P power integrabl is a main approach to of Lebesgue square in solve the second category of integral equation. Via researching on tegrable functions, the set of continuous functions and the set of e functions, Riesz found that the set from the others. These laid the foundation for the appearance of of Lebesgue square integrable functions is different Banach space theory and the dual space theory.