From Uniform Continuity to Absolute Continuity
Classical Analysis and ODEs
2015-03-17 v2
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.
Keywords
Cite
@article{arxiv.1011.6471,
title = {From Uniform Continuity to Absolute Continuity},
author = {Kai Yang and Chenhong Zhu},
journal= {arXiv preprint arXiv:1011.6471},
year = {2015}
}