Hamel‐isomorphic images of the unit ball |
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| Authors: | Jacek Cichoń Przemysław Szczepaniak |
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| Affiliation: | 1. Institute of Mathematics and Computer Science, Technical University of Wroc?aw,Wybrze?e Wyspiańskiego 27, 50‐370 Wroc?aw, Poland;2. Institute of Mathematics and Computer Sciences, University of Opole, ul. Oleska 48, 45‐052 Opole, Poland |
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| Abstract: | In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ?2 and ?. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non‐measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non‐measurable (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Lebesgue measure Baire property null set non‐measurable set. |
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