From Uniform Continuity to Absolute Continuity

Details From Uniform Continuity to Absolute Continuity From Uniform Continuity to Absolute Continuity

2010-11-30

arxiv.org/abs/1011.6471v2

Mathematics

Classical Analysis and ODEs

Scientific paper

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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