Absolutely Continuous Real Function has Derivative Almost Everywhere

Theorem

Let $I \subseteq \R$ be a real interval.

Let $f$ be an absolutely continuous real function on $I$.

Then $f$ has a derivative almost everywhere on $I$.

Proof

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Sources

• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): absolutely continuous