Some aspects of the measure extension problem

Abstract

In this chapter, we concisely present several versions of the general measure extension problem which is a special case of the problem of extending partial real-valued functions, envisaged in the preceding chapter. Undoubtedly, the measure extension problem is important in many questions of analysis and probability theory. Among various aspects of this problem the following three should be especially distinguished: purely set-theoretical, algebraic, and topological. Below, we will touch upon each of the above-mentioned aspects and will show their specific features.