关键词: 连续函数, 积分的绝对连续性, Lebesgue测度, 介值定理

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