Volterra's function is a function $f\colon\mathbb{R}\to\mathbb{R}$ such that:

  • $V$ is differentiable,

  • $V'$ is bounded,

  • $V'$ is not Riemann-integrable.


Is every Volterra's function unbounded?

I've searched the site and found some results, like

What is an example that a function is differentiable but derivative is not Riemann integrable

Bounded Function Which is Not Riemann Integrable

but is doesn't deal with boundedness of a function.


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