@article{53fbac544e5c433eaf5ab2dc30bf4751,
title = "A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory",
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",
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",
year = "2017",
doi = "https://doi.org/10.14321/realanalexch.42.2.0385",
language = "الإنجليزيّة",
volume = "42",
pages = "385--390",
journal = "Real Analysis Exchange",
issn = "0147-1937",
publisher = "Michigan State University Press",
number = "2",
}