Real Analysis Exchange

A Positive Function with Vanishing Lebesgue Integral in Zermelo-Fraenkel Set Theory

Vladimir Kanovei and Mikhail Katz

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Abstract

Can a positive function on \(\mathbb{R}\) have zero Lebesgue integral? It depends on how much choice one has.

Article information

Source
Real Anal. Exchange, Volume 42, Number 2 (2017), 385-390.

Dates
First available in Project Euclid: 10 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.rae/1525917693

Digital Object Identifier
doi:10.14321/realanalexch.42.2.0385

Mathematical Reviews number (MathSciNet)
MR3721807

Zentralblatt MATH identifier
06870335

Subjects
Primary: 03E25: Axiom of choice and related propositions
Secondary: 28A25: Integration with respect to measures and other set functions

Keywords
Lebesgue integral Zermelo-Fraenkel theory Feferman-Levy model

Citation

Kanovei, Vladimir; Katz, Mikhail. A Positive Function with Vanishing Lebesgue Integral in Zermelo-Fraenkel Set Theory. Real Anal. Exchange 42 (2017), no. 2, 385--390. doi:10.14321/realanalexch.42.2.0385. https://projecteuclid.org/euclid.rae/1525917693


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