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2004-2005 Convergence of sequences of functions having some generalized Pawlak properties.
Zbigniew Grande
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Real Anal. Exchange 30(2): 581-588 (2004-2005).


A function $f:\mathbb R \to \mathbb R$ has the property ${\mathcal M}_1$ (${\mathcal M}_2$) if the restricted function $f | D(f)$ ($f | D_{ap}(f)$) is monotone. ($D(f)$ $D_{ap}(f)$ denotes the set of all discontinuity points [the set of all approximate discontinuity points] of $f$.) In this article I investigate the uniform, pointwise and transfinite limits of sequences of functions with the property ${\cal M}_i$, $i = 1,2$.


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Zbigniew Grande. "Convergence of sequences of functions having some generalized Pawlak properties.." Real Anal. Exchange 30 (2) 581 - 588, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 15 October 2005

zbMATH: 1119.26006
MathSciNet: MR2177420

Primary: 26A15 , 26B05

Keywords: density topology , measurability , monotone functions , pointwise convergence , sequences of functions , Uniform convergence

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 2 • 2004-2005
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