My question is maybe elementary but I'm having troubles with it. I have a function $f$ absolutely continuous in (a,c) and in (c,b), $f$ continuous in $c$. Is $f$ absolutely continuous in (a,b)?
2026-04-24 09:34:57.1777023297
Basic Question about absolutely continuous functions
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Correct! All your have to prove is that if $f$ is continuous at c then it is absolutely continuous at c. Then,consider a random $x_0$ that belongs to (a,c) and prove that $f$ is absolutely continuous.