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Cantor function (Definition)
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"Cantor function" is owned by jirka.
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See Also: Cantor set, singular function

Other names:  Cantor ternary function, Cantor-Lebesgue function, Devil's staircase
Also defines:  Cantor function, Cantor ternary function
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Cross-references: pathological, areas, similar, iterations, Calculus, graph, complement, almost everywhere, monotonic, continuous, function, real number, Cantor set, singular function, canonical
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This is version 6 of Cantor function, born on 2004-02-08, modified 2007-12-12.
Object id is 5554, canonical name is CantorFunction.
Accessed 14377 times total.

Classification:
AMS MSC26A30 (Real functions :: Functions of one variable :: Singular functions, Cantor functions, functions with other special properties)

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Devil's staircase by archibal on 2004-04-06 21:01:49
A nice article on Cantor's function (the Devil's staircase) finishes with a tanatlizing comment: Such functions turn up in many areas of mathematics and are not just pathological examples.

Nice to say that, but it really provokes the question: where do they turn up?

The only example I can think of off-hand is of locally constant functions on $p$-adic fields, and that's a bit iffy: the base field is pretty different from $\mathbb{R}$.

I suppose they provide a counterexample for the simplest interpretation of the Fundamental Theorem of Calculus, but that hardly helps them qualify as non-pathological.
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