Kempisty's theorem for the integral product quasicontinuity

Zbigniew Grande

Zbigniew Grande

Colloquium Mathematicae, Tome 106 (2006), p. 257-264 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $| (1 / μ (U \cap I)) \int_{U \cap I} f (t) d t - f (x) | < r$ . Kempisty’s theorem concerning the product quasicontinuity is investigated for the above notions.

Publié le : 2006-01-01

Zbl 1113.26012

EUDML-ID : urn:eudml:doc:286524

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     title = {Kempisty's theorem for the integral product quasicontinuity},
     journal = {Colloquium Mathematicae},
     volume = {106},
     year = {2006},
     pages = {257-264},
     zbl = {1113.26012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-6}
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Zbigniew Grande. Kempisty's theorem for the integral product quasicontinuity. Colloquium Mathematicae, Tome 106 (2006) pp. 257-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-6/