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Eurasian Mathematical Journal, 2013, Volume 4, Number 3, Pages 63–69
(Mi emj133)
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New examples of Pompeiu functions
G. A. Kalyabin Faculty of Physical, Mathematical, and Natural Sciences, Peoples’ 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.
Received: 15.04.2013
Citation:
G. A. Kalyabin, “New examples of Pompeiu functions”, Eurasian Math. J., 4:3 (2013), 63–69
Linking options:
https://www.mathnet.ru/eng/emj133 https://www.mathnet.ru/eng/emj/v4/i3/p63
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Abstract page: | 323 | Full-text PDF : | 183 | References: | 49 |
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