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

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