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Nate River
Nate River
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Is there a singular function that is Hölder continuous of anyevery order less than $1$?

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Iosif Pinelis
Iosif Pinelis
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We say a non-constant function $f$ on $[0, 1]$ is singular if it is continuous, and in addition differentiable almost everywhere with $f' = 0$ a.e.

Does there exist a singular function that is Hölder continuous of order $\alpha$ for all $\alpha < 1$?

We say a function $f$ on $[0, 1]$ is singular if it is continuous, and in addition differentiable almost everywhere with $f' = 0$ a.e.

Does there exist a singular function that is Hölder continuous of order $\alpha$ for all $\alpha < 1$?

We say a non-constant function $f$ on $[0, 1]$ is singular if it is continuous, and in addition differentiable almost everywhere with $f' = 0$ a.e.

Does there exist a singular function that is Hölder continuous of order $\alpha$ for all $\alpha < 1$?

Source Link
Nate River
Nate River
  • 6.2k
  • 2
  • 23
  • 99

Is there a singular function that is Hölder continuous of any order less than $1$?

We say a function $f$ on $[0, 1]$ is singular if it is continuous, and in addition differentiable almost everywhere with $f' = 0$ a.e.

Does there exist a singular function that is Hölder continuous of order $\alpha$ for all $\alpha < 1$?