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1996/1997 On Borel measurable functions that are VBG and (N)
Vasile Ene
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Real Anal. Exchange 22(2): 688-695 (1996/1997).


The Banach-Zarecki Theorem states that \(VB \cap (N) = AC\) for continuous functions on a closed set. Hence it is a linear space. In this article we show that \(VB \cap (N)\) is a linear space on any real Borel set. Hence \(VBG \cap (N)\) will also be a real linear space for Borel measurable functions defined on an interval. As a consequence of this result, we show that the \(AK_N\) integral of Gordon (\cite{G14}) is well defined. We also give answers to Gordon’s questions in \cite{G14}.


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Vasile Ene. "On Borel measurable functions that are VBG and (N)." Real Anal. Exchange 22 (2) 688 - 695, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 22 May 2012

zbMATH: 0942.26019
MathSciNet: MR1460981

Primary: 26A24 , 26A39

Keywords: \((N)\) , \([{\mathcal C}G]\) , \({\mathcal C}_{ap}\) , \(AC\) , \(ACG\) , \(VB\) , \(VBG\) , Borel sets

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 2 • 1996/1997
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