ABSTRACT
It is well known that the notion of measurability of sets and functions plays an important role in various fields of classical and modern analysis (also, in probability theory and general topology). For functions of several variables, a related notion of sup-measurability was introduced and investigated (see, e.g., [3], [8], [38], [41], [67], [96], [101], [104], [106], [115], [116], [176], [187], [188] and the references given therein). It turned out that this notion can successfully be applied to some topics from analysis and, in particular, to the theory of ordinary differential equations (for more information concerning applications of sup-measurable mappings in the above-mentioned theory, see [116] and Chapter 17 of this book).
