Geodesic
New examples of Pompeiu functions
Eurasian mathematical journal, Tome 4 (2013) no. 3, pp. 63-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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For given sequence of real numbers $\{x_k\}^\infty_1\subset I:=[0,1]$ the explicitly defined function $\varphi\colon I\to I$ is constructed such that $\varphi(x_k)=0$, $k\in\mathbb N$, $\varphi(x)>0$ a.e. and all $x\in I$ are Lebesgue points of $\varphi(\cdot)$. So its primitive $f(\cdot)$ is an everywhere differentiable strictly increasing function with $f'(x_k)=0$, $k\in\mathbb N$. 
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     author = {G. A. Kalyabin},
     title = {New examples of {Pompeiu} functions},
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G. A. Kalyabin. New examples of Pompeiu functions. Eurasian mathematical journal, Tome 4 (2013) no. 3, pp. 63-69. http://geodesic.mathdoc.fr/item/EMJ_2013_4_3_a5/

[1] A. Bruckner, Differentiation of Real Functions, Springer Verlag, 1978 | MR | Zbl

[2] D. Pompeiu, “Sur les fonctions dérivées”, Math. Ann., 63 (1906), 326–332 | DOI | MR

[3] A. Denjoy, “Sur les fonctions dérivées sommable”, Bull. Soc. Math. France, 43 (1915), 161–248 | MR | Zbl

[4] B. M. Makarov, M. G. Goluzina, A. A. Lodkin, A. N. Podkorytov, Selected problems in real analysis, Saint Petersburg, 2004 (in Russian) | MR

[5] I. P. Natanson, Theory of functions of real variable, Nauka, Moscow, 1974 (in Russian) | MR