Journal article

Approach regions of Lebesgue measurable, locally bounded, quasi-continuous functions

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Author list: Daghighi, Abtin

Publication year: 2012

Start page: 659

End page: 680

Number of pages: 22

ISSN: 1312-8876


Abstract

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.


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