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The properties of convex functions are of interest. I would like to know that if every convex function is of bounded variation?

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No, take $f(x)=e^x$ on $\mathbb R$, or $g(x) = \frac1{x(1-x)}$ on $(0,1)$.

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  • $\begingroup$ Why $f(x)=e^x$ is not of bounded variation? $\endgroup$
    – Ali
    Aug 11, 2015 at 7:22
  • $\begingroup$ because it is not integrable on the real lline $\endgroup$
    – daw
    Aug 11, 2015 at 8:11

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