A peculiar set in the plane constructed by Vituškin, Ivanov and Melnikov
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.
compact set in the plane with positive linear measure
scientific article; zbMATH DE number 756674