A peculiar set in the plane constructed by Vituškin, Ivanov and Melnikov (Q1890627)
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scientific article; zbMATH DE number 756674
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A peculiar set in the plane constructed by Vituškin, Ivanov and Melnikov |
scientific article; zbMATH DE number 756674 |
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A peculiar set in the plane constructed by Vituškin, Ivanov and Melnikov (English)
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19 November 1995
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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.
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Hausdorff measure
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compact set in the plane with positive linear measure
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contraction
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measure functions
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