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Eurasian Math. J., 2013, Volume 4, Number 3, Pages 63–69 (Mi emj133)  

New examples of Pompeiu functions

G. A. Kalyabin

Faculty of Physical, Mathematical, and Natural Sciences, Peoplesí Friendship University of Russia, 117198 Moscow, Miklukho-Maklaya 6

Abstract: 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 $f'(x_k)=0$, $k\in\mathbb N$.

Keywords and phrases: everywhere differentiable functions, strict monotonicity, dense zero set of a derivative, upper semi-continuity, Lebesgue points.

Full text: PDF file (388 kB)
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MSC: 26A24, 26A30, 26A42
Received: 15.04.2013
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Citation: G. A. Kalyabin, “New examples of Pompeiu functions”, Eurasian Math. J., 4:3 (2013), 63–69

Citation in format AMSBIB
\Bibitem{Kal13}
\by G.~A.~Kalyabin
\paper New examples of Pompeiu functions
\jour Eurasian Math. J.
\yr 2013
\vol 4
\issue 3
\pages 63--69
\mathnet{http://mi.mathnet.ru/emj133}


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