Set of points of non-differentiability

Question

As an exercise I proved that if $f: \mathbb R \to \mathbb R$ is a function then the set of discontinuities of $f$ must be an $F_\sigma$ set. I thought it was an interesting result.

Now I am wondering: is there a result like this for points of non-differentiability of $f$? If $N_f$ denotes the set of points where $f$ is not differentiable does $N_f$ have to be of a certain type?

For continuous function $f$, the set of discontinuities $N_f$ is countable union of $G_\delta$'s. — Shine, Jul 11 '14 at 12:55
See my answer to Continuous functions are differentiable on a measurable set?. — Dave L. Renfro, Jul 11 '14 at 14:03
@DaveL.Renfro Thank you. In your answer does "does not have finite derivative" mean the same as "is not differentiable"? — blue, Jul 17 '14 at 14:08
If so maybe you could post the link to your other answer as an answer here so I can accept it. — blue, Jul 17 '14 at 14:15

score 1 · Accepted Answer · edited Apr 13 '17 at 12:19

1

As you asked in a comment, I'm posting my comment as an answer.

The answer to your question about $N_f$ is given in my answer to Continuous functions are differentiable on a measurable set?.

edited Apr 13 '17 at 12:19

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answered Jul 17 '14 at 15:10

Dave L. Renfro

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Set of points of non-differentiability

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