If $f:[a,b]\rightarrow R$ is a uniformly continuous function
then is it true that $f$ is always absolutely continuous?
2026-04-02 06:43:30.1775112210
If $f:[a,b]\rightarrow R$ is a uniformly continuous function then its absolutely continuous?
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No, consider $f(x) = x\sin(\frac 1x)$ with $f(0) = 0$ on $[0,1]$.