Local operators in some subspaces of the space \(L_0\) (Q1589057)

The authors discuss so-called local operators in the sense of \textit{I. V. Shragin} [Dokl. Akad. Nauk SSSR 227, No. 1, 47-49 (1976; Zbl 0338.47035)] in spaces of measurable functions. In particular, they give a condition, both necessary and sufficient, for a local operator which is continuous in measure to be a Nemytskij operator generated by some Carathéodory functions. The results are both deep and interesting, but the English translation of the Russian original is very poor and makes the reading difficult and unpleasant.