R^n中的Jordan测度与重积分

Jordan Measure and Multiple Integral in Rn

本文介绍重积分的一般理论,首先讨论了R^n中点集的体积(Jofdan测度),然后通过上积分与下积分建立R^n中的积分概念并讨论其性质,最后严格证明了n重积分的换元法则。

This paper deals with the general theory of multiple integral. We discuss the volume of a set(Jordan measure),define the concept of integral in R^n by upper-integral and lower-integral and go further into the properties of integral, with the principle of change of variables strictly proved.