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In [1, page 7], the author says.

Kolmogorov showed that if the function $$f(x) = \sum_{n=1}^{\infty} \frac{\cos 3^n x}{3^n}$$ has a finite or infinite generalized derivative on a set of positive measure, then the function is nonmeasurable.

Where can I find a proof/explanation of this result (and/or other similar results) in English? The reference doesn't have to be to Kolmogorov's orignal paper; for example, a modern exposition would suffice (and might very well be better).

[1] A. N. Shiryaev, "Andrei Nikolaevich Kolmogorov", Theory of Probability and Applications, vol 34, no. 1, 1988.

Note that I also posted this question on MathOverflow. Since it's just a reference request, I don't think cross-posting is a big deal in this case.

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If you have a proof in Russian, I can write its translation in English – Norbert Jan 27 '12 at 17:12
The only one I have so far is in French: 'Sur la possibilite de la definition generale de la derivee, de l'integrale et de la sommation des series divergentes', C.R. Acad. Sci. Paris 180(1925), 362-364. – Quinn Culver Jan 27 '12 at 18:42
So you should rewrite your question as "Help me translate this French article"... – Norbert Jan 27 '12 at 19:03
@Norbert I assume this work (or work including examples (with proof) of other such functions) should already exist in English. I'd rather look for that before I trouble someone with translating. – Quinn Culver Jan 27 '12 at 19:14
Are any of the answers on MathOverflow acceptable to you? If so, you might want to consider accepting one of them. – Michael Albanese Dec 21 '15 at 6:44
up vote 1 down vote accepted

This question has been asked and answered on MathOverflow. I have replicated the accepted answer by Raymond Manzoni below.

A translation in english is in "Selected Works of A.N. Kolmogorov I" : "On the possibility of a general definition of derivative, integral and summation of divergent series" (page 33 and 34).

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