S. Ruziewicz and W. Sierpińnski in 1933 proved that each function$f :\mathbb{R} \to\mathbb{R}$can berepresented as a superposition of two measurable functions. Here the strengthening ofthis theorem is given. The properties of Lusin set are studied and microscopic Hamelbases are considered.
@article{266,
title = {On some problem of Sierpi\'nski and Ruziewicz concerning the superposition of measurable functions. Microscopic Hamel basis.},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v58i0.266},
language = {EN},
url = {http://dml.mathdoc.fr/item/266}
}
Karasińska, Aleksandra; Wagner-Bojakowska, Elżbieta. On some problem of Sierpiński and Ruziewicz concerning the superposition of measurable functions. Microscopic Hamel basis.. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v58i0.266. http://gdmltest.u-ga.fr/item/266/