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2002-2003 On natural functions and Lipschitz functions.
Marek Małolepszy
Author Affiliations +
Real Anal. Exchange 28(1): 249-258 (2002-2003).


We give certain characterizations of the so-called natural functions introduced by Chistyakov. We show that the set of natural functions from $[a, b]$ into a normed space $X$ is small in the porosity sense in the set of uniform Lipschitz 1 functions with the norm inherited from the space of $BV$ functions. The sizes of other classes of Lipschitz functions in $BV$ are also established.


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Marek Małolepszy. "On natural functions and Lipschitz functions.." Real Anal. Exchange 28 (1) 249 - 258, 2002-2003.


Published: 2002-2003
First available in Project Euclid: 12 June 2006

zbMATH: 1063.26005
MathSciNet: MR1973985

Primary: 26A16 , 26A45

Keywords: Bounded variation , Lipschitz functions , natural functions

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 1 • 2002-2003
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