Kempisty's theorem for the integral product quasicontinuity

Zbigniew Grande. "Kempisty's theorem for the integral product quasicontinuity." Colloquium Mathematicae 106.2 (2006): 257-264. <http://eudml.org/doc/286524>.

@article{ZbigniewGrande2006,
abstract = {A function f: ℝⁿ → 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 ∋ x open in the Euclidean topology of ℝⁿ (resp. strong density topology, ordinary density topology) there is an open set I such that I ∩ U ≠ ∅ and $|(1/μ (U∩I)) ∫_\{U∩I\} f(t)dt - f(x)| < r$. Kempisty’s theorem concerning the product quasicontinuity is investigated for the above notions.},
author = {Zbigniew Grande},
journal = {Colloquium Mathematicae},
keywords = {Lebesgue measure; upper (lower) strong/ordinary density; (measurable) quasicontinuous and integrally (strongly; ordinarily) quasicontinuous function; section; countable ordinal; transfinite induction},
language = {eng},
number = {2},
pages = {257-264},
title = {Kempisty's theorem for the integral product quasicontinuity},
url = {http://eudml.org/doc/286524},
volume = {106},
year = {2006},
}

TY - JOUR
AU - Zbigniew Grande
TI - Kempisty's theorem for the integral product quasicontinuity
JO - Colloquium Mathematicae
PY - 2006
VL - 106
IS - 2
SP - 257
EP - 264
AB - A function f: ℝⁿ → 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 ∋ x open in the Euclidean topology of ℝⁿ (resp. strong density topology, ordinary density topology) there is an open set I such that I ∩ U ≠ ∅ and $|(1/μ (U∩I)) ∫_{U∩I} f(t)dt - f(x)| < r$. Kempisty’s theorem concerning the product quasicontinuity is investigated for the above notions.
LA - eng
KW - Lebesgue measure; upper (lower) strong/ordinary density; (measurable) quasicontinuous and integrally (strongly; ordinarily) quasicontinuous function; section; countable ordinal; transfinite induction
UR - http://eudml.org/doc/286524
ER -