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

Can a positive function on R have zero Lebesgue integral? It depends on how much choice one has. Mathematical Reviews subject classification: Primary: 03E25; Secondary: 28A25 Key words: Lebesgue integral, Zermelo–Fraenkel theory, Feferman–Levy model

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Bibliographic Details
Published inReal analysis exchange Vol. 42; no. 2; pp. 385 - 390
Main Authors Kanovei, Vladimir, Katz, Mikhail
Format Journal Article
LanguageEnglish
Published East Lansing Michigan State University Press 01.01.2017
Subjects
Axiom of choice
Integrals
Lebesgue measures
Mathematical functions
Mathematical integrals
Mathematical set theory
Mathematics
Measure theory
Musical intervals
Null set
Riemann integrals
Set theory
Sigma additivity
Theory
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Summary:Can a positive function on R have zero Lebesgue integral? It depends on how much choice one has. Mathematical Reviews subject classification: Primary: 03E25; Secondary: 28A25 Key words: Lebesgue integral, Zermelo–Fraenkel theory, Feferman–Levy model
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0147-1937
1930-1219
DOI:10.14321/realanalexch.42.2.0385