ABSTRACT
In the present chapter we would like to discuss deep relationships between the following two fundamental concepts of mathematical analysis: measurability and continuity. For this purpose, some nontrivial examples are given below, which underline close connections between measurable and continuous real-valued functions, and the reader will see how those connections can be described in terms of absolutely nonmeasurable functions and universal measure zero sets (cf. Chapter 5 where these notions are introduced and examined).
