On some Problem of Sierpiński and Ruziewicz Concerning the Superposition of Measurable Functions. Microscopic Hamel Basis
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15. Aug. 2014
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Online veröffentlicht: 15. Aug. 2014
Seitenbereich: 91 - 99
Eingereicht: 28. Nov. 2013
DOI: https://doi.org/10.2478/tmmp-2014-0008
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© 2014
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
S. Ruziewicz and W. Sierpiński proved that each function f : ℝ → ℝ can be represented as a superposition of two measurable functions. Here, a strengthening of this theorem is given. The properties of Lusin set and microscopic Hamel bases are considered