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2001/2002 Local and Global Monotonicity
Szymon Głąb
Real Anal. Exchange 27(2): 765-772 (2001/2002).


We give characterizations of sets $E\subset[0,1]$ for which the local monotonicity of each function $f:[0,1]\to\mathbb{R}$ from a given class $\mathcal{F}$, at all points $x\in E$, implies the global monotonicity of $f$ on $[0,1]$. We consider as $\mathcal{F}$ -- the families of continuous functions, differentiable functions, absolutely continuous functions, functions of class $C^n$ ($n=1,2,...,\infty$), real analytic functions and polynomials.


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Szymon Głąb. "Local and Global Monotonicity." Real Anal. Exchange 27 (2) 765 - 772, 2001/2002.


Published: 2001/2002
First available in Project Euclid: 2 June 2008

zbMATH: 1044.26008
MathSciNet: MR1923166

Primary: 26A48
Secondary: 26A15 , 26A42 , 26A46

Keywords: Cantor set , Cantor--Bendixson derivative , condition (N) of Luzin , local monotonicity , Monotonicity

Rights: Copyright © 2001 Michigan State University Press

Vol.27 • No. 2 • 2001/2002
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