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arXiv · 1011.6471

From Uniform Continuity to Absolute Continuity

Kai Yang·Chenhong Zhu
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Abstract

Absolute continuity implies uniform continuity, but generally not vice versa. In this short note, we present one sufficient condition for a uniformly continuous function to be absolutely continuous, which is the following theorem: For a uniformly continuous function f defined on an interval of the real line, if it is piecewise convex, then it is also absolutely continuous.

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Kai Yang, Chenhong Zhu. 2010-12-06. From Uniform Continuity to Absolute Continuity. https://arxiv.org/abs/1011.6471

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