On the Nemytskii conjecture (Q2366410)

The author discusses the validity of the Nemytskij conjecture for standard functions \(f: T\times X\to Y\), where \(T\) is a complete measure space, \(X\) is a Suslin space, and \(Y\) is a separable metric space. Related work is due to \textit{I. Vrkoč} [Czechosl. Math. J. 19(94), 99- 109 (1969; Zbl 0175.147)], \textit{A. V. Ponosov} [Dokl. Akad. Nauk SSSR 289, No. 6, 1308-1311 (1986; Zbl 0618.47055)], and \textit{P. P. Zabrejko} and the reviewer [J. Austral. Math. Soc., Ser. A 47, No. 2, 186-210 (1989; Zbl 0683.47045)].