What is the example of a continuous function which is not an indefinite integral?

Asked Jun 30 '15 at 09:58

Active Jun 30 '15 at 09:58

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By Royden's Real Analysis (3rd), chap 5. Thm 14, it reads that

'A function F is an indefinite integral if and only if it is absolutely continuous. '

What is the continuous but absolutely-DISconinuous function which is not an indefinite integral of any other function?

asked Jun 30 '15 at 09:58

Outis Choi

I can imagine the Weierstrass function will fit. But there is probably much simpler examples. – Surb Jun 30 '15 at 10:00
2

Cantor staircase function. – Martigan Jun 30 '15 at 10:01
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Probably it's clearer to write "not absolutely continuous," rather than "absolutely discontinuous," which sounds badly pathological. – Travis Willse Jun 30 '15 at 10:09

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