含参量瑕积分一致收敛的判别法及其性质

The Discriminant Method and Properties of Uniform Convergence of Parametric Defect Integral

摘要: 含参量瑕积分在数学分析的多元函数积分学中有着非常重要的作用，大多数教材中对于含参量无穷积分一致收敛的判别法及其性质给出了详细的介绍及其证明，但大多数教材只给出了含参量瑕积分一致收敛的定义，然而对于大多数学生而言含参量瑕积分一致收敛性的判别及其性质是不容易易理解和掌握的，因此，本文根据课本中含参量无穷积分一致收敛的判别法及其性质的证明给出了含参量瑕积分一致收敛性判别法的定义与证明及其基本性质的定义与证明。

Abstract: Parametric integral plays a very important role in the integration of multiple functions in mathe-matical analysis. Most textbooks give a detailed introduction to the discriminant method and prop-erties of uniform convergence of parametric infinite integral and its proof, but most textbooks only give the definition of uniform convergence of parametric integral. However, for most students, it is not easy to understand and master the identification and properties of uniform convergence of in-tegral with parameter. Therefore, this paper gives the definition and proof of the identification and properties of uniform convergence of integral with parameter and infinite integral with parameter in the textbook.