CAJ | 학술논문

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.
적분제일중치정리화제이중치정리시정적분이론중량개십분중요적정리,근년래관우기내점성적토론비상엄범.수선근거련속함수적개치정리,용일충신방법증명적분제일중치정리적내점성;연후제출일개실례,설명적분제이중치정리재통상조건하불구유내점성;최후이용정적분존재적충요조건화Abel변환적수단,증명적분제이중치정리재가상일개비상일반화적조건시구유내점성.
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 inte?gral 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.