Lebesgue测度的介值定理及其应用  

Intermediate value theorem of lebesgue measure and its applications

作　　者：路慧芹[1] 路婕 LU Huiqin;LU Jie(School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China)

机构地区：[1]山东师范大学数学与统计学院,山东济南250014

出　　处：《山东科学》2018年第6期97-99,共3页Shandong Science

基　　金：山东省自然科学基金(ZR2018MA022)

摘　　要：利用连续函数的介值性和Lebesgue测度的单调性得到了Lebesgue测度具有介值性质,并利用所得结果证明了Lebesgue积分的绝对连续性的逆命题也是成立的。By using the intermediate value property of continuous functions and the monotone of Lebesgue measure,we obtain that Lebesgue measure possesses the property of intermediate value.As an application,we prove that the inverse proposition of absolute continuity of Lebesgue integral is true.

关 键 词：LEBESGUE测度 连续函数 介值定理 积分的绝对连续性 

分 类 号：O172.12[理学—数学]