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2016 On the Property N-1
Stanisław Kowalczyk, Małgorzata Turowska
Abstr. Appl. Anal. 2016: 1-5 (2016). DOI: 10.1155/2016/1256906


We construct a continuous function f:[0,1]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.


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Stanisław Kowalczyk. Małgorzata Turowska. "On the Property N-1." Abstr. Appl. Anal. 2016 1 - 5, 2016.


Received: 2 November 2015; Accepted: 7 February 2016; Published: 2016
First available in Project Euclid: 13 April 2016

zbMATH: 1355.54020
MathSciNet: MR3473169
Digital Object Identifier: 10.1155/2016/1256906

Rights: Copyright © 2016 Hindawi

Vol.2016 • 2016
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