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The whole problem is: Find a function that is in Bounded variation(BV) but not in Absolutely Continuous(AC). It's not too hard to find a function is in BV, but how do we prove a function is not AC?

Martin Sleziak
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Wade
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1 Answers1

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You can take Cantor function. See details here: https://en.wikipedia.org/wiki/Cantor_function

Virtuoz
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  • But I don't know how to show it's not absolutely continuous, what should it need to prove? – Wade Dec 10 '16 at 17:19