Hamel‐isomorphic images of the unit ball
Copyright policy )Hamel‐isomorphic images of the unit ball
AbstractIn this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ℝ2 and ℝ. 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)
- University of Wrocław Poland
- Polish Academy of Sciences Poland
- University of Opole Poland
- Wrocław University of Science and Technology Poland
- Institute of Computer Science Poland
Lebesgue measure, Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, Consistency and independence results, nonmeasurable set, Baire property
Lebesgue measure, Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, Consistency and independence results, nonmeasurable set, Baire property
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