两个积分中值定理内点性的新证明  

New Prove of Interior Point Property for Two Integral Mean Value Theorems

作　　者：余显志[1] 肖光强[1] 赵胜利[1] 

机构地区：[1]后勤工程学院基础部,重庆401311

出　　处：《后勤工程学院学报》2013年第2期88-90,96,共4页Journal of Logistical Engineering University

摘　　要：积分第一中值定理和第二中值定理是定积分理论中两个十分重要的定理,近年来关于其内点性的讨论非常广泛。首先根据连续函数的介值定理,用一种新方法证明积分第一中值定理的内点性;然后提出一个实例,说明积分第二中值定理在通常条件下不具有内点性;最后利用定积分存在的充要条件和Abel变换的手段,证明积分第二中值定理在加上一个非常一般化的条件时具有内点性。The first and second integral mean value theorem are two important theorems in definite integral theory, and the discussion about the interior point property is also very extensive in recent year. At first, the interior point property of the first integral mean value theorem is proved with a new method using intermediate value theorem of continuous function. Then the second in- tegral mean value theorem without interior point property is illustrated by proposing an example under normal conditions. At last, the interior point property of the second integral mean value theorem plus a very general condition is proved by using the necessary and sufficient conditions for the existence of definite integral and the method of Abel transformation.

关 键 词：连续 介值定理 中值定理 内点性 ABEL变换 

分 类 号：O172.2[理学—数学]