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I'm reading the proof that continuous second derivative is symmetric

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In the proof below, the authors utilize the continuity of $\partial^2 f$, but from this question, I got that we do not need the continuity of $\partial^2 f$.

My question: How to modify the below proof to the case $\partial^2 f$ is not continuous? Thank you so much for your help!

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Akira
  • 17,367

0 Answers0