A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory

Vladimir Kanovei; Mikhail Katz

doi:10.14321/realanalexch.42.2.0385

A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory

Vladimir Kanovei, Mikhail Katz

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Can a positive function on ℝ have zero Lebesgue integral? It depends on how much choice one has.

Original language	English
Pages (from-to)	385-390
Number of pages	6
Journal	Real Analysis Exchange
Volume	42
Issue number	2
DOIs	https://doi.org/10.14321/realanalexch.42.2.0385
State	Published - 2017

Bibliographical note

Funding Information:
Mathematical Reviews subject classification: Primary: 03E25; Secondary: 28A25 Key words: Lebesgue integral, Zermelo–Fraenkel theory, Feferman–Levy model Received by the editors March 1, 2017 Communicated by: Krzysztof Ciesielski ∗The research for this paper was supported in part by the RFBR grant number 17-01-00705 †The research for this paper was supported by the Israel Science Foundation grant number 1517/12

Keywords

Feferman-Levy model
Lebesgue integral
Zermelo-Fraenkel theory

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10.14321/realanalexch.42.2.0385

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abstract = "Can a positive function on ℝ have zero Lebesgue integral? It depends on how much choice one has.",

keywords = "Feferman-Levy model, Lebesgue integral, Zermelo-Fraenkel theory",

author = "Vladimir Kanovei and Mikhail Katz",

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doi = "10.14321/realanalexch.42.2.0385",

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KW - Feferman-Levy model

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A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory

Abstract

Bibliographical note

Keywords

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