<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In the present paper, we introduce the notion of classes of <italic>ρ</italic>-upper continuous functions. We show that <italic>ρ</italic>-upper continuous functions are Lebesgue measurable and, for <italic>ρ &lt; </italic>1/2 , may not belong to Baire class 1. We also prove that a function with Denjoy property can be non-measurable.</p></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.

A note on ρ-upper continuous functions

Institute of Mathematics Academia Pomeraniensis ul. Arciszewskiego 22b PL–76-200 Słupsk POLAND

Tatra Mountains Mathematical Publications

{"article-title":"A note on ρ-upper continuous functions"}

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...

A note on ρ-upper continuous functions

Published Online: Nov 12, 2012

Page range: 153 - 158

DOI: https://doi.org/10.2478/v10127-009-0055-0

Keywords
density of a set at a point, continuous functions, measurable functions, path continuity, Denjoy property, Baire class 1.

This content is open access.

A note on ρ-upper continuous functions

Published Online: Nov 12, 2012

Page range: 153 - 158

DOI: https://doi.org/10.2478/v10127-009-0055-0

Keywordsdensity of a set at a point, continuous functions, measurable functions, path continuity, Denjoy property, Baire class 1.

This content is open access.

Keywords
density of a set at a point, continuous functions, measurable functions, path continuity, Denjoy property, Baire class 1.