On the property \(N^{- 1}\)
type: Item
instance of: scholarly article
title: On the property \(N^{- 1}\)
zbMATH Open document ID: 1470.26007
DOI: 10.1155/2016/1256906
author: Małgorzata Turowska
author: Stanisław Kowalczyk
published in: Abstract and Applied Analysis
publication date: 2018-08-30T00:00:00Z
review text: Summary: We construct a continuous function \(f : [0,1] \rightarrow \mathbb{R}\) such that \(f\) possesses \(N^{- 1}\)-property, but \(f\) does not have approximate derivative on a set of full Lebesgue measure. This shows that Banach's Theorem concerning differentiability of continuous functions with Lusin's property \((N)\) does not hold for \(N^{- 1}\)-property. Some relevant properties are presented.
Mathematics Subject Classification ID: 26A27
zbMATH DE Number: 6929339
Wikidata QID: Q59121496
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/1256906
OpenAlex ID: W2288867015
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description: scientific article; zbMATH DE number 6929339