A note on ρ-upper continuous functions

Stanisław Kowalczyk; Katarzyna Nowakowska

doi:10.2478/v10127-009-0055-0

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A note on ρ-upper continuous functions

Tatra Mountains Mathematical Publications

Volume 44 (2009): Issue 1 (December 2009)

By: Stanisław Kowalczyk and Katarzyna Nowakowska

Open Access

|Nov 2012

Abstract

In the present paper, we introduce the notion of classes of ρ-upper continuous functions. We show that ρ-upper continuous functions are Lebesgue measurable and, for ρ < 1/2 , may not belong to Baire class 1. We also prove that a function with Denjoy property can be non-measurable.

References

[1] BRUCKNER, A. M.: Differentiation of Real Functions, Lecture Notes in Math., Vol. 659, Springer-Verlag, New York, 1978.10.1007/BFb0069821
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[2] BRUCKNER, A. M.-O’MALLEY, R. J.-THOMSON, B. S.: Path derivatives: a unifiedview of certain generalized derivatives, Trans. Amer. Math. Soc. 283 (1984), 97-125.10.1090/S0002-9947-1984-0735410-1
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Articles in this issue

DOI: https://doi.org/10.2478/v10127-009-0055-0 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

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Language: English

Page range: 153 - 158

Published on: Nov 12, 2012

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

density of a set at a point,

continuous functions,

measurable functions,

Related subjects:

© 2012 Stanisław Kowalczyk, Katarzyna Nowakowska, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Volume 44 (2009): Issue 1 (December 2009)