Let $g$ be an absolutely continuous function that maps the interval $[a,b]$ into itself and $f$ be absolutely continuous on $[a,b]$. Is it true that the composition $f(g)$ is absolutely continuous?. It is true if $g$ is increasing or decreasing (see Fremlin's Theory of measure), and it is obviously true if $g$ is in $Lip_1[a,b]$. I do not know if it is true in general, neither was I able to find a counterexample in the literature.
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