On the N. N. Luzin theorem (Q5896645)

The well-known classical Luzin's theorem on approximation of measurable functions by continuous functions is extended. This extension is related to \(\mu\)-measurable functions \(f: X\to Y\), where \(\mu\) is the Radon measure on \(X\), \(X\) is a locally compact separable metric space and \(Y\) is a complete separable metric space which is an absolute neighbourhood retract. The paper is a continuation of some previous author's results published in Sib. Mat. Zh. 27, No. 6, 210-215 (1986; Zbl 0613.54005) and Mat. Zametki 38, No. 1, 89-81 (1985; Zbl 0595.54002).