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A long paused dialog cache *****

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C: This is not an antiderivative of the zero function.
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L: Yes, such cannot grow too much on small sets.
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H&K: To be precise, only on such where no derivative is.
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B&M: Definitely, its out of any monotone control.
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Hint below.
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Hint: CaLeHeKuBeMa
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Notice that the Cantor function ( EN ) covers the Measure & integration theory (modulo trivia).
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Observe that f'(x)=0 on A where |A|=1/3 + 2/9 + 4/27 + ... = 1.
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By the way, the Cantor function corresponds to many hockey matches: almost nothing happens in the middle third, moreover almost nothing happens in the middle thirds of the remaining thirds, ...
Wink