A remark about Laczkovich's theorem on functions whose sections are derivatives
type: Item
instance of: scholarly article
title: A remark about Laczkovich's theorem on functions whose sections are derivatives
zbMATH Open document ID: 0631.26003
DOI: 10.1007/BF01848106
published in: Periodica Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: \textit{M. Laczkovich} [Period. Math. Hung. 12, 243-254 (1981; Zbl 0449.26009)] has proved that each real function of two real variables all of whose sections in both coordinates are derivatives, is Lebesgue measurable. In this paper, the author constructs a real function of two real variables which is not Lebesgue measurable and all of whose sections of the function in both coordinates belong to the Preiss class \(M^*_ 3\) [\textit{D. Preiss}, Trans. Am. Math. Soc. 272, 161-184 (1982; Zbl 0508.26001)].
reviewed by: Ladislav Mišík
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 28A20
zbMATH DE Number: 4025740
zbMATH Keywords: nonmeasurable functions
zbMATH Keywords: Zahorski classes
zbMATH Keywords: Lebesgue measurable functions
zbMATH Keywords: sections of functions of two variables
zbMATH Keywords: Preiss class \(M^ *_ 3\)
author: Jan Stanisław Lipiński
MaRDI profile type: Publication
cites work: Level Sets of Derivatives
cites work: Sur La Premiere Derivee
full work available at URL: https://doi.org/10.1007/bf01848106
OpenAlex ID: W1997403029
description: scientific article; zbMATH DE number 4025740