A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory
Classical Analysis and ODEs
2017-05-02 v1 Logic
Abstract
Can a positive function on R have zero Lebesgue integral? It depends on how much choice one has. Keywords: Lebesgue integral; Zermelo--Fraenkel theory; Feferman-Levy model
Keywords
Cite
@article{arxiv.1705.00493,
title = {A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory},
author = {Vladimir Kanovei and Mikhail G. Katz},
journal= {arXiv preprint arXiv:1705.00493},
year = {2017}
}
Comments
6 pages, to appear in Real Analysis Exchange