SHANDONG SCIENCE ›› 2018, Vol. 31 ›› Issue (6): 97-99.doi: 10.3976/j.issn.1002-4026.2018.06.015

• Other Research Article • Previous Articles     Next Articles

Intermediate value theorem of lebesgue measure and its applications

LU Hui-qin,LU Jie   

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China
  • Received:2018-05-27 Published:2018-12-20 Online:2018-12-20

Abstract:

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.

Key words: intermediate value theorem, Lebesgue measure, absolute continuity of integral, continuous function

CLC Number: 

  • O174.12

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