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2004-2005 Descriptive properties of σ-porous sets.
Miroslav Zelený
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Real Anal. Exchange 30(2): 547-564 (2004-2005).


The main aim of this paper is to construct an absolutely continuous function with non-$\sigma$-porous graph. This answers the question posed by Foran, whether there exists a function of bounded variation with non-$\sigma$-porous graph. As a consequence we obtain a positive solution of Goffman’s question, whether there exists a function with non-$\sigma$-porous graph such that its Fourier series converges uniformly.


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Miroslav Zelený. "Descriptive properties of σ-porous sets.." Real Anal. Exchange 30 (2) 547 - 564, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 15 October 2005

MathSciNet: MR2177425

Primary: 26A45 , 28A05

Keywords: $\sigma$-porosity , absolutely continuous functions , functions pf bounded variation

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 2 • 2004-2005
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