The problem on the measure of the union of line segments in the plane with restrictions on the set of their ends
type: Item
instance of: scholarly article
title: The problem on the measure of the union of line segments in the plane with restrictions on the set of their ends
zbMATH Open document ID: 1482.28003
author: A. E. Lipin
publication date: 2021-12-08T00:00:00Z
review text: The paper consider the following question: let \(\varphi\) be bijection between two zero measure sets \(A\) and \(B\) of the unit interval. If \(S(A, B, \varphi)\) denotes the union of all segment in the plane with endpoints \((a, 0)\) and \((\varphi(a), 1)\), for some \(a \in A\), what about the measure of \(S(A, B, \varphi)\)? The paper is written in Russian, thus it is not accessible to everyone.
reviewed by: Daniele Puglisi
Mathematics Subject Classification ID: 28A75
zbMATH DE Number: 7440283
zbMATH Keywords: measure
zbMATH Keywords: plane
MaRDI profile type: Publication
full work available at URL: semi.2021.18.101
OpenAlex ID: W4205724726
cites work: Q5781238
cites work: The Kakeya Problem for Simply Connected and for Star-Shaped Sets
cites work: Q5610889
cites work: An improved bound for Kakeya type maximal functions
cites work: New bounds for Kakeya problems
cites work: An improved bound on the Hausdorff dimension of Besicovitch sets in ℝ³
cites work: Besicovitch type maximal operators and applications to Fourier analysis
cites work: The multiplier problem for the ball
cites work: Q3415147
cites work: Set Theory
cites work: Q4323294
cites work: Q4150804
DOI: 10.33048/SEMI.2021.18.101
published in: Sibirskie Elektronnye Matematicheskie Izvestiya
description: scientific article; zbMATH DE number 7440283