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{{Use American English|date = March 2019}}
{{Short description|Continuous function that is not absolutely continuous}}
[[File:CantorEscalier-2.svg|thumb|right|400px|The graph of the Cantor function on the [[unit interval]] ]]
In [[mathematics]], the '''Cantor function''' is an example of a [[function (mathematics)|function]] that is [[continuous function|continuous]], but not [[absolute continuity|absolutely continuous]]. It is a notorious [[Pathological_(mathematics)#Pathological_example|counterexample]] in analysis, because it challenges naive intuitions about continuity, derivative, and measure. Though it is continuous everywhere and has zero derivative almost everywhere, its value still goes from 0 to 1 as its argument reaches from 0 to 1. Thus, in one sense the function seems very much like a constant one which cannot grow, and in another, it does indeed monotonically grow.
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