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2004-2005 On the convergence of sequences of integrally quasicontinuous functions.
Zbigniew Grande
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Real Anal. Exchange 30(2): 767-778 (2004-2005).


A function $ f: \mathbb{R}^n \to \mathbb{R}$ satisfies condition $(Q_i(x))$ (resp. $(Q_s(x))$, [$Q_o(x)$]) at a point $x$ if for each real $r > 0$ and for each set $U \ni x$ belonging to the Euclidean topology in $\mathbb{R} ^n$ (resp.~to the strong density topology [to the ordinary density topology]) there is an open set $I$ such that $I \cap U \neq \emptyset $, $f$ is Lebesgue integrable on $I\cap U$ and $$\left|\frac{1}{\mu (U\cap I)}\int_{U \cap I} f(t)dt - f(x) \right| < r.$$ These notions are modifications of quasicontinuity or approximate quasicontinuity. In this article we investigate the limits of sequences of such functions.


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Zbigniew Grande. "On the convergence of sequences of integrally quasicontinuous functions.." Real Anal. Exchange 30 (2) 767 - 778, 2004-2005.


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

zbMATH: 1118.26012
MathSciNet: MR2177433

Primary: 26A03 , 26A15 , 26B05

Keywords: Density topologies , integral quasicontinuities , Quasicontinuity , sequences of functions

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 2 • 2004-2005
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