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On sets of points of approximate continuity and ϱ-upper continuity

Anna Kamińska, Katarzyna Nowakowska and Małgorzata Turowska
From the journal Mathematica Slovaca

Abstract

In the paper some properties of sets of points of approximate continuity and ϱ-upper continuity are presented. We will show that for every Lebesgue measurable set E ⊂ ℝ there exists a function f : ℝ → ℝ which is approximately (ϱ-upper) continuous exactly at points from E. We also study properties of sets of points at which real function has Denjoy property. Some other related topics are discussed.

MSC 2010: Primary 26A15; 54C30

  1. Communicated by L’ubica Holá

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Received: 2019-05-20
Accepted: 2019-08-26
Published Online: 2020-03-10
Published in Print: 2020-04-28

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