<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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</p></abstract>

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

On some Problem of Sierpiński and Ruziewicz Concerning the Superposition of Measurable Functions. Microscopic Hamel Basis

University of Łódź Faculty of Mathematics and Computer Science ul. Banacha 22 PL–90-238 Łódź POLAND

Tatra Mountains Mathematical Publications

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...

On some Problem of Sierpiński and Ruziewicz Concerning the Superposition of Measurable Functions. Microscopic Hamel Basis

Published Online: Aug 15, 2014

Page range: 91 - 99

Received: Nov 28, 2013

DOI: https://doi.org/10.2478/tmmp-2014-0008

Keywords
microscopic sets, nullsets, sets of the first category, sets having the Baire property, Lusin set, Hamel basis

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On some Problem of Sierpiński and Ruziewicz Concerning the Superposition of Measurable Functions. Microscopic Hamel Basis

Published Online: Aug 15, 2014

Page range: 91 - 99

Received: Nov 28, 2013

DOI: https://doi.org/10.2478/tmmp-2014-0008

Keywordsmicroscopic sets, nullsets, sets of the first category, sets having the Baire property, Lusin set, Hamel basis

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
microscopic sets, nullsets, sets of the first category, sets having the Baire property, Lusin set, Hamel basis