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Approach regions of Lebesgue measurable, locally bounded, quasi-continuous functions
Mid Sweden University, Faculty of Science, Technology and Media, Department of applied science and design.ORCID iD: 0000-0001-7488-8004
2012 (English)In: International Journal of Mathematical Analysis, ISSN 1312-8876, E-ISSN 1314-7579, Vol. 6, no 13, p. 659-680Article in journal (Refereed) Published
Abstract [en]

Quasi-continuity (in the sense of Kempisty) generalizes directional continuity of complex-valued functions on open subsets of ℝ n or ℂ n, and in particular provides certain approach regions at every point. We show that these can be used as a proof tool for proving several properties forLebesgue measurable, locally bounded, quasi-continuous functions e.g. that for such a function f the polynomial ring C(M,K)[f] (where K = ℝ or ℂ) satisfies that the equivalence classes under identification a.e. have cardinality one and an asymptotic maximum principle.

Place, publisher, year, edition, pages
2012. Vol. 6, no 13, p. 659-680
Keywords [en]
Approach regions; Locally bounded lebesgue measurable quasi-continuous functions
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:miun:diva-15999Scopus ID: 2-s2.0-84865142026OAI: oai:DiVA.org:miun-15999DiVA, id: diva2:510134
Available from: 2012-03-15 Created: 2012-03-15 Last updated: 2017-12-07Bibliographically approved

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Daghighi, Abtin

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