Abstract
A function $f : \mathbb{R}^n \to \mathbb{R}$ satisfies condition $(Q_{r,i}(x))$ (resp. ($Q_{r,s}(x))$, [$Q_{r,o}(x)$]) at a point $x$ if for each real $r > 0$ and for each set $U$ containing $x$ and belonging to Euclidean topology in $\mathbb{R} ^n$ (resp. to the strong density topology [to the ordinary density topology]) there is a regular domain $I$ such that int$(I) \cap U \neq \emptyset $, $f\!\restriction\!I$ is integrable in the sense of Riemann and $|\frac{1}{\mu (U\cap I)}\int_{U \cap I} f(t)\,dt - f(x)| < r$. These notions are particular cases of their analogues for the Lebesgue integral. In this article we compare these notions with the classical quasicontinuity and integral quasicontinuities
Citation
Zbigniew Grande. "On Riemann integral quasicontinuity.." Real Anal. Exchange 31 (1) 239 - 252, 2005-2006.
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