Real Analysis Exchange

On the Sup-Measurable Functions Problem

Marek Balcerzak

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Abstract

We show some results connected with the problem whether it is consistent that every sup-measurable function \(F\colon\mathbb{R}^2\to\mathbb{R}\) is measurable. We will also relate this problem to a von Weizsäcker problem concerning a generalization of Blumberg’s theorem.

Article information

Source
Real Anal. Exchange, Volume 23, Number 2 (1999), 787-798.

Dates
First available in Project Euclid: 14 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1337001386

Mathematical Reviews number (MathSciNet)
MR1639981

Zentralblatt MATH identifier
0940.28004

Subjects
Primary: 26B30: Absolutely continuous functions, functions of bounded variation
Secondary: 04A15 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 54H05.

Keywords
{Lebesgue measurability} {Baire property} {sup-measurable function.}

Citation

Balcerzak, Marek. On the Sup-Measurable Functions Problem. Real Anal. Exchange 23 (1999), no. 2, 787--798. https://projecteuclid.org/euclid.rae/1337001386


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