On the Marcinkiewicz theorem for the binary Perron integral (Q1358471)

\textit{K. M. Ostaszewski} [Mem. Am. Math. Soc. 253 (1986; Zbl 0596.26005)] and \textit{B. S. Thomson} [Mem. Am. Math. Soc. 452 (1991; Zbl 0734.26003)] have defined the concept of a differential base in order to use it in defining generalized derivates. By using the latters in the definition of majorants and minorants, one obtains generalizations of the Perron integral. The author shows that the validity of the Marcinkiewicz theorem (= a measurable function is Perron integrable iff it has continuous majorants and minorants) depends on the choice of the differential base.