Kempisty's theorem for the integral product quasicontinuity
Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 257-264
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
A function $f:\mathbb R ^n \to \mathbb R$
satisfies the 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 $U \ni x$
open in the Euclidean topology of $\mathbb R^n$ (resp.
strong density topology, ordinary density topology)
there is an open set $I$ such
that $I \cap U \neq \emptyset $ and
$|(1/\mu (U\cap I))\int_{U \cap I}
f(t)\,dt - f(x)| r$.
Kempisty's theorem concerning the product quasicontinuity
is investigated for the above notions.
Keywords:
function mathbb mathbb satisfies condition resp point each real each set euclidean topology nbsp mathbb resp strong density topology ordinary density topology there set cap neq emptyset cap int cap kempistys theorem concerning product quasicontinuity investigated above notions
Affiliations des auteurs :
Zbigniew Grande 1
@article{10_4064_cm106_2_6,
author = {Zbigniew Grande},
title = {Kempisty's theorem for the integral product quasicontinuity},
journal = {Colloquium Mathematicum},
pages = {257--264},
publisher = {mathdoc},
volume = {106},
number = {2},
year = {2006},
doi = {10.4064/cm106-2-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm106-2-6/}
}
TY - JOUR AU - Zbigniew Grande TI - Kempisty's theorem for the integral product quasicontinuity JO - Colloquium Mathematicum PY - 2006 SP - 257 EP - 264 VL - 106 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/cm106-2-6/ DO - 10.4064/cm106-2-6 LA - en ID - 10_4064_cm106_2_6 ER -
Zbigniew Grande. Kempisty's theorem for the integral product quasicontinuity. Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 257-264. doi: 10.4064/cm106-2-6
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