关于测度的教学探究

Teaching Explorations on Measure

本文对《实变函数》中的重要概念测度的教学作了若干探究。既要从直观上介绍Lebesgue测度的原始定义,也要使学生明白Lebesgue的原始定义依赖于原集合的性质而不能进行推广的缺陷。在此基础上更要强调Caratheodory的定义脱离了原集合的具体性质便于进一步抽象推广。

In this paper, some teaching explorations on important concept measure in function of real variable are done. It is necessary not only the original definition of measure should be introduced, but also the fault of this definition depending on the specific properties of point sets should be pointed out. Furthermore, it is crucial to be emphasized that the definition of measure based on the Caratheodory condition is convenient to be generalized since this definition separates itself from the concrete characters of point sets.