On some Problem of Sierpiński and Ruziewicz Concerning the Superposition of Measurable Functions. Microscopic Hamel Basis
et | 15 août 2014
Tatra Mountains Mathematical Publications
Real Functions ‘13 Real Functions, Topology, Real and Functional Analysis, Locally Convex Spaces
À propos de cet article
Publié en ligne: 15 août 2014
Pages: 91 - 99
Reçu: 28 nov. 2013
DOI: https://doi.org/10.2478/tmmp-2014-0008
Mots clés
© 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