## Real Analysis Exchange

### On Borel measurable functions that are VBG and (N)

Vasile Ene

#### Abstract

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}.

#### Article information

Source
Real Anal. Exchange, Volume 22, Number 2 (1996), 688-695.

Dates
First available in Project Euclid: 22 May 2012

https://projecteuclid.org/euclid.rae/1337713150

Mathematical Reviews number (MathSciNet)
MR1460981

Zentralblatt MATH identifier
0942.26019

#### Citation

Ene, Vasile. On Borel measurable functions that are VBG and (N). Real Anal. Exchange 22 (1996), no. 2, 688--695. https://projecteuclid.org/euclid.rae/1337713150

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