In mathematics, the Cantor function is an example of a function that is continuous but not absolutely continuous. It is a well-known counterexample in analysis: although it is continuous everywhere and has a derivative of zero almost everywhere, its value still rises from 0 to 1 as its argument goes from 0 to 1, so despite appearing constant it in fact grows monotonically. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Origin YearGeorg Cantor (1884) introduced the Cantor function Connections
Attributed To
Source Cantor Function (Wikipedia)
In Branch
Source Cantor Function (Wikipedia)
Is Kind Of Object
Sources
1. Cantor Function (Wikipedia)
Lead section
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous.
Attributed To: Giuseppe Vitali, Lead paragraph
called the Cantor ternary function, the Lebesgue function, Lebesgue's singular function, the Cantor-Vitali function, the Devil's staircase, the Cantor staircase function, and the Cantor-Lebesgue function. Georg Cantor (1884) introduced
In Branch: Analysis, Lead paragraph
It is a notorious counterexample in analysis, because it challenges naive intuitions about continuity, derivative, and measure.
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