A peculiar set in the plane constructed by Vituškin, Ivanov and Melnikov
type: Item
instance of: scholarly article
title: A peculiar set in the plane constructed by Vituškin, Ivanov and Melnikov
zbMATH Open document ID: 0826.28006
author: Tamás Keleti
published in: Real Analysis Exchange
publication date: 1995-11-19T00:00:00Z
review text: The author constructs a compact set in the plane with positive linear measure that cannot be mapped using a contraction onto a segment. The paper is based on the ideas of \textit{A. G. Vituškin}, \textit{L. D. Ivanov} and \textit{M. S. Mel'nikov} [Dokl. Akad. Nauk SSSR 154, 1256-1259 (1963; Zbl 0138.037)] who sketched proofs of the existence of such a set. The main concept is related to the definition of measure functions published by Kolmogorov in 1932.
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 756674
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: compact set in the plane with positive linear measure
zbMATH Keywords: contraction
zbMATH Keywords: measure functions
reviewed by: Ilya S. Molchanov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 756674